Graham explains, "It's a good problem to have, but the challenge of having Firmino in your team is that he excelled in the false-nine role. It was difficult to find another player like him, and it became a never-ending quest for us at Liverpool."
Firmino scored nine goals in Liverpool's title-winning season but he was the facilitator who helped Mohamed Salah and Sadio Mane score 19 and 18, respectively. He dropped deep, lured defenders in, and was a pivotal figure in that potent Liverpool front three.
Graham and his colleagues understood that it was not as simple as bringing in a player who could do what Firmino could do while scoring more. The alchemy at play among that forward trio was difficult to recreate. A free-scoring striker would come at a cost.
"It was not an automatic calculation where we would say, if we bring this player in then Mo will get one fewer shot per game and that translates into so many more goals for them but maybe a couple fewer for Mo. But we did do that work on a bespoke basis."
TrendingGraham, speaking to following the release of his book, How to Win the Premier League, talks of a team's possession "like a sort of production line" - a process by which a side is able to deliver the ball to the player who ultimately scores the goal.
"You need players who can win the ball back to start a possession," he explains. "You need players who can make that possession safe and then progress it forward. You need players who can open up the defence and then someone to put the ball in the net."
He acknowledges that Liverpool were more fortunate than most in that they had the resources to find players with broader skillsets - capable of doing more than one of these things. "I made a point in the book about triple threats," says Graham.
"If you can pass, dribble and shoot, it means you are more likely to be able to play anywhere across the forward line. That helps with squad depth. It also makes you difficult to defend against and means you have to worry less about that production line."
Diogo Jota, the player currently operating as Liverpool's de facto centre-forward this season under Arne Slot, represents the most successful attempt yet to pivot away from Firmino, who left the club in the summer of 2023. Jota has 57 goals for Liverpool.
Not bad for a player who was seen as anything but a sure thing when signed for £45m in 2020. "He was kind of underrated," suggests Graham. Indeed, Jota was not even a guaranteed starter at previous club Wolves. There was uncertainty over his position.
"I remember we had a lot of internal discussions about it. It was not quite the same as the Firmino discussion, but it was a question of, like, well, who is he? Is he a striker? He played as one of the two up front at Wolves and liked to drift wide and cut in quite a lot.
"If you looked at the formation, Jota was a striker in one of two centre-forward positions, but because of how he interpreted that, it looked as though he could play on the left and he could certainly play as a centre-forward if we wanted him as a true centre-forward.
"He was a really interesting one because we did go back and forth with the video analysis department. We knew he didn't play in the formation as a wide forward, but the way he interpreted that role did make him look more like a Liverpool wide forward."
That was the target, someone who was capable of scoring from those zones. "What we wanted, for as close to a Mane or a Mo replacement as possible, was a wide forward. They are not a striker, they stay wide, but they cut in and have a high shooting volume."
Initially, Jota was defined by his differences with Firmino. "He is not as all-round a player as Firmino is, but he is a much better finisher than Firmino is, so those skills complement each other." More recently, playing centrally, similarities have emerged.
Jota's pressing has been a feature of Liverpool's encouraging start to the season under Slot. Statistically, he has covered 1.72 kilometres while closing down defenders during the press - which is more than any other Premier League player so far this season.
He has also been a part of the team's press more than any other Premier League player - doing so 76 times already. It is telling that Dominik Szoboszlai and Luis Diaz are also among the top five - but it is Jota, the most advanced player, who triggers that press.
"He can play the Firmino role, even if he does not quite have the same passing game as Firmino," says Graham. "That is no criticism of Jota. Very few players do." Nevertheless, he has created more turnovers through his pressing than any other forward this season.
Jota and Salah combined for the first goal of the Slot era against Ipswich but it is notable that the Portuguese creates space for the Egyptian, albeit in a different way to Firmino. He retains that tendency to drift left, which opens up the channel for Salah.
It is just another reason why he has been preferred by Slot thus far. But there is still a wildcard option for the Liverpool manager. Darwin Nunez has a role to play - even if his particular skillset is less multi-functional. "Darwin really is a centre-forward."
Graham describes Nunez as the last Liverpool signing that he worked on, a parting gift who still divides opinion as he enters his third season at Anfield and approaches a century of appearances. "With Darwin, there is still that role question," says Graham.
"Darwin looked like one of the best young strikers in Europe. Haaland was the obvious one, but he was out of Liverpool's financial range. The transfer fee is not that big a component of the total spend on Haaland. So, Haaland was out of the equation.
"Darwin was a centre-forward who did centre-forward things. So the question was, Firmino's getting older and we are going to have to replace him eventually. Would the coach be comfortable with the slight change of style that Darwin is going to bring?"
That change has been no more than a qualified success so far, Nunez's finishing being described as "unacceptable" by Jamie Carragher. And yet, the chances keep coming. Nunez had a shot more regularly than any other Premier League player last season.
"I can only see it from the outside now, so I don't have any special insight into it, but the interesting thing is that with the amount of shots Darwin takes, you would expect him to be taking some from Mo, but he doesn't seem to be taking that many shots from Mo."
Indeed, Salah still ranks fourth on that list himself, his own adaptability a testament to his greatness. Graham has not given up on Nunez. "Finishing is always a bit of a noisy business," he says. "And Liverpool's shot generation looks good with him in the team."
Liverpool never did find a way of replacing Firmino like for like. But in acquiring two very different players who are capable of operating in that centre-forward position, and with the help of Salah somehow maintaining his own levels, perhaps they will not need to.