The midfielder has struggled for regular action since joining the Partenopei from Sunderland in the summer of 2016, playing just 60 minutes this season.
A move away from the Stadio San Paolo is expected in January and Giaccherini's agent, Furio Valcareggi, has revealed he almost joined Fiorentina in the summer.
Valcareggi says there has been a "misunderstanding" between his player and the club and has suggested Atalanta could be ready to give his career a fresh start.
"He'll definitely leave Napoli," he told Premium Sport. "We were happy at Napoli, but there was a misunderstanding about his role and he has barely played since Euro 2016.
"Emanuele is still in good shape, he hasn't lost a shred of his usefulness and he's still very much being considered in January. Atalanta like him a lot, but I haven't had contact with them."