Diakite, who spent the second half of last season on loan at Fiorentina, is surplus to requirements at Sunderland and did not even receive a squad number following his return from Italy.
Black Cats boss Poyet claims 10 clubs are chasing the former Lazio defender, with Fiorentina joined by fellow Italian sides Palermo, Sampdoria and Inter Milan in a race to sign the Frenchman.
“Diakite has got 10 options,” Poyet told the Sunderland Echo.
“The problem is managing them because he has got his priorities as well.”
David Moberg Karlsson and Alfred N’Diaye have already departed Sunderland as Poyet clears his squad out with Cabral and Graham set to follow.
Cape Verde midfielder Cabral is eager to remain in England, while Graham has been linked with newly-promoted Championship side Wolves as well as former clubs Middlesbrough and Watford.
“I think we’re getting close to moving them on because of the transfer window,” Poyet added.
“I have to give them credit. We were very close to finding a solution for them (Diakite and Cabral) before we went to Portugal for pre-season - and Danny as well.
“That was why they didn’t travel. It was not like ‘off you go’.”