It is believed that Mignolet has told Paolo Di Canio he will not sign a new contract at the Stadium of Light and wants to leave in order to boost his 2014 World Cup ambitions.
Liverpool could be in need of a goalkeeper given that speculation continues to link their current number one Jose Reina with Barcelona.
Sunderland, though, will not be keen to sell Mignolet, who was their Player of the Year in the 2012/13 season.
But the 25-year-old, who has also been linked with Arsenal, has only two years remaining on his contract and Sunderland will know his value will decrease as time drags on.
However, the North-East club would still want at least £9m from Liverpool, who have also been linked with Stoke City's Asmir Begovic.