Giaccherini looks set for the Sunderland exit this summer.
Giaccherini spent the second half of last season on loan from Sunderland at Bologna having had a disappointing two seasons at the Stadium of Light, with the second season blighted by injury problems.
The report says Torino have reached an agreement with Sunderland of around €2 million (£1.7 million), and it is now up to the player to make a decision surrounding his future.
It seems the Italian's days are numbered at the club as manager Sam Allardyce seems to be planning for the season ahead without the 31-year-old in his plans.
Giaccherini has had an impressive time of things at Euro 2016 with Italy as they have been one of the stand-out sides in their run to the quarter-finals, although they missed out on a place in the last four to Germany on penalties.
After that, the player may want to sit tight and see if any other offers come his way, and his agent could well be working on that, especially as he has been quoted saying that it would be 'a dream' for the player to link up with Antonio Conte - who managed Italy during the European Championship - at Chelsea, as reported by ESPN.
As far as Sunderland are concerned, it looks as if they are getting the player off their books this summer, with some money in return.