Arsene Wenger is thought to see the Belgian as an ideal back-up stopper, and somebody who provide a challenge to first-choice Wojciech Szczesny.
The Frenchman has a number of goalkeeping options already, but is unconvinced by the likes of Lukasz Fabianski and Vito Mannone, both of whom have enjoyed spells between the sticks in recent seasons.
A bid of £5m is being prepared by the North Londoners, but it remains unclear as to whether the Black Cats will be willing to part company with their man, who has kept six clean sheets this season.
It had been thought that Wenger was considering a move for Liverpool’s Pepe Reina, but the Spaniard would likely cost around £20m.
Mignolet has been a solid performer for the Stadium of Light-based club since his arrival in 2010.
The 24-year-old profited heavily from the injury woes of former Sunderland goalkeeper Craig Gordon, to become first-choice at the club.
If a move does materialise next month, it’s likely that Wenger will allow Fabianski to leave the club in search of regular football.
Mannone could be also be allowed to move on, although the Gunners are likely to want keep hold of the Italian as a back-up option.