Giaccherini has spent this past season out on loan back in Italy with Bologna and he enjoyed a good season in Serie A.
He was a regular for Roberto Donadoni’s team, making 28 appearances in total and scoring seven goals, more than he has managed since joining the Black Cats back in 2013.
Bologna are keen to have him back permanently, with the player and his agent both having spoken about a possible return next season.
They are not the only Italian side keen on him either, with Lazio and Fiorentina also having been linked with him in recent months.
A stay at Sunderland is also a possibility as Sam Allardyce assesses his squad this summer.
According to them the Hornets, who have just confirmed Italian Walter Mazzarri as their new manager, could be eyeing a move for €2million, around £1.5million.