Mignolet was axed for the visit of Arsenal this afternoon.
The Belgian has started the campaign as Jurgen Klopp's No.1 but Loris Karius replaced him between the sticks at Anfield today.
And Italian news outlet Gianluca Di Marzio now claim Napoli are keen on a deal for Mignolet.
It's claimed the Serie A giants have contacted the ex-Sunderland man about a potential switch.
Former Liverpool star Pepe Reina is Napoli's current first-choice keeper, but he's wanted by French side Paris St-Germain.
Di Marzio add Liverpool appear unlikely to let Mignolet leave, despite the interest in the 29-year-old.
Kop legend Graeme Souness says Mignolet's axing was not a case of him being 'rested' by Klopp.
“It’s not something I’ve heard or seen before, two league games in,” Souness said on Sky Sports.
“I’m not sure if resting is the right term.
“For me, unless he’s had an injury or an argument, I think it has to be that he really doesn’t fancy Mignolet that much and he’s going to get Karius up to speed just in case, or when he has to start using him.
“So it’s four games for a goalkeeper, four games where he’s had to concentrate.
“Physically it’s not demanding, but you have to be concentrated.
“Buffon, all the top goalkeepers, you don’t rest them. I think he’s preparing for the day when Mignolet makes a few mistakes and he wants to have a go with this guy, so he’s trying to keep him up to speed.
“I just don’t see how resting is the right word to use. I don’t see that as the right reason either.”
Any deal will have to be done by 11pm on Thursday, when the transfer window closes.
Mignolet has been at Anfield since Brendan Rodgers signed him in 2013.
