The Italian defender has spent the day at the Serie A club's Castelvolturno training ground in Caserta and is expected to put pen to paper imminently.
Dossena joined Liverpool from Udinese in the summer of 2008 for £7million, but failed to impress despite a memorable goal in the 4-1 win at Man Utd last season.
An official announcement from Napoli is expected within the next few hours.
