Giaccherini has been linked with a move back to Italy for much of the summer.
Italy's Emanuele Giaccherini celebrates after scoring their first goal
Giaccherini has been continuously linked with a move to Serie A after becoming surplus to requirements at the Stadium of Light. He spent last season away from the club on loan at Bologna.
Emanuele Giaccherini of Sunderland
The report says that a deal of 1.5 million Euros (£1.26 million) has been agreed between the two clubs, and has even gone as far to say the deal is 'done'.
It will be welcome for Sunderland to get a player off their books as things haven't worked out for him at the Stadium of Light and to get a transfer fee for him which can be a small contribution to the club's transfer kitty for the season ahead, though it is a loss on the £6.5 million they paid for him back in 2013.
Italy's Emanuele Giaccherini scores their first goal
One or two impressive performances for Italy at Euro 2016 may have attracted Napoli's attention, and the 31-year-old could be rewarded with a season of Champions League football.
The same source had reported that Torino had expressed their interest in the player but they look set to miss out on his signature.
For one reason or the other it didn't work out for Giaccherini at Sunderland, but his performances at the European Championships for his country show that he can play a big part in a side that suits him.
Sunderland's Emanuele Giaccherini