Isak, now rated by Newcastle at £150m, was available from Real Sociedad at the time for £63m, while Liverpool paid over £85m to take Nunez from Benfica.
Recalling Klopp's decision, Graham told the Financial Times: "Jurgen created a lot of success for the club, so it’s understandable why it moved in that direction (from data-driven decisions to managerial preference).
"I’m happy to talk about my colleagues persuading Jurgen (in 2017) that Mohamed Salah was the player to buy instead of Julian Brandt."
Jurgen preferred Nunez
Graham also said, "In 2022, he signed Darwin Nunez (for £64m plus add-ons) instead of Alexander Isak.
"Both players, if you look at top young centre-forwards in Europe, they would be number one and two — or two and three but (Erling) Haaland was going to (Manchester) City and out of our price range.
"Jurgen preferred Nunez. It would be very churlish of me to say, 'It’s terrible that Jurgen had his choice', when in the past Jurgen had been persuaded by me and my colleagues of a different choice.
"And it was still the case that we signed good players — in Nunez’s case, one of the best young strikers in Europe."