The Belgium goalkeeper declared yesterday his "situation could not continue" after being dropped for victory over Manchester City on Sunday.
Het Nieuwsblad says Napoli are prepared to offer €20m for Mignolet.
The Reds keeper would move to Naples as a long-term replacement for Pepe Reina, who is off contract in June.
Mignolet stated yesterday: “I always try to stay quiet and calm. In the past I did come back stronger from such situations.
"But I must of course also think of my own future. The only thing I can do is focus on my training and do my best. I become 30 years old and the World Cup is coming this summer.
"This situation cannot take too long, which is clear. I cannot lose any more time."