PSG are also interested in the 22-year-old, who scored 17 goals and provided 14 assists in all competitions last season.
Leverkusen are reluctant to sell one of their best players, but they would listen to offers of £50m.
Diaby's contract at the Bundesliga club does not expire until 2025.
For his part, Diaby would be open to leaving Leverkusen this summer.
Eddie Howe must now make a decision on whether he wants to spend a large portion of his summer budget on Diaby.
New Magpies sporting director Dan Ashworth is said to very keen on the youngster.
Leverkusen chief Simon Rolfes recently said: "We want to keep Moussa for as long as possible.
"We do not have any offers but we are not even looking for that.
"We would like to keep him and play with him next year in the Champions League."