Former A.S. Roma star Alisson completed a £56m move to Anfield earlier this summer as Liverpool looked to sign a long-term solution to one of their biggest problem areas over the last few seasons.
However, the Brazil international's arrival has left goalkeepers Mignolet and Loris Karius uncertain of their future on Merseyside.
Although it now seems increasingly likely that manager Jürgen Klopp will hold onto Karius as his second choice goalkeeper, Mignolet's agent has appeared to issue a come-and-get-me plea to Carlo Ancelotti's Napoli.
"Mignolet likes Napoli and the admiration is not new," Nico Vaesen told Radio Kiss Kiss Napoli (via Inside Futbol). "Napoli have enquired about the boy on several occasions in previous transfer windows.
"However, there is nothing guaranteed about his move to Napoli at the moment and we will have to wait for the next few days to see whether they will make an offer. Considering that the market will close soon, they will have to make a move soon if we want to further the negotiations for everyone to reach an agreement."
However, Napoli president Aurelio de Laurentiis might need some convincing before launching a move for Mignolet. The Partenopei have already signed goalkeepers Alex Meret and Orestis Karnezis from Udinese, while Nikita Contini has also returned from a loan spell away from the club.