Speculation indicates that Reds boss Jurgen Klopp has not been convinced by Mignolet since his arrival on Merseyside and was set to offload him either in January or at the end of the season.
According to The Guardian, the Reds are set to offer an increase on the £60,000-a-week deal the 27-year-old is currently on.
Additionally, Klopp spoke on Tuesday about Mignolet and how he has no plans to replace the former Sint-Truiden gloveman.
"We are not looking for another goalkeeper," said Klopp ahead of Wednesday night's Capital One Cup quarter-final with Southampton.
"We have enough high-quality goalkeepers, I've had a lot of goalkeepers over the last few years and Simon Mignolet is one of the smartest I have ever had.
"He is completely open and he's young enough to develop, to improve. He's not had the easiest situation before I came here, but since I have been here there has been nothing to criticise, absolutely nothing."