The Belgian international has been heavily linked with a move away from the Stadium of Light this summer, after an impressive individual 2012/13 campaign for the struggling Black Cats.
Paolo Di Canio will be keen to retain the 25-year-old's services ahead of next season, but appears to be fighting a losing battle, with Mignolet's head turned by reported admirers.
Gunners boss Arsene Wenger is said to be keen on adding the goalkeeper to his Emirates Stadium ranks, as he looks to bolster his first-team options between the sticks in north London.
Meanwhile, Brendan Rodgers has also been credited with an interest in luring Mignolet to Anfield, as speculation continues to surround the long-term future of Liverpool's current number one, Pepe Reina.
With two years still to run on his current deal at Sunderland, the Wearside club are in a strong position when it comes to negotiating his exit. However, there is little point in keeping any player against his will, and so will listen to offers of around £10million.
"I think it is very unlikely that he will sign a new contract," confirmed the player's agent, Nico Vaesen. "Simon has obviously come to a point where he wants to step up a level and there is a lot of interest in him.
"He is very ambitious and wants to play in the World Cup, in Brazil, next year.
"It was a good thing that Sunderland stayed up and it is a fantastic club where he has had three great years. But it is maybe time to step up a level and play for a club competing for a European spot."