The Belgium shot-stopper has been linked with a number of clubs in the Premier League, with Arsenal reported to be weighing up a move.
Wojciech Szczesny is currently Arsene Wenger's first-choice at the Emirates with Lukasz Fabianski and Vito Mannone being used as back-up.
The Frenchman is keen to bring in somebody who can push the Poland international and has been linked with a £5million January move for 24-year-old Mignolet, who has kept seven Premier League clean sheets this season.
Mignolet: "I am trying to avoid all the rumours at the minute. We will see what happens at the end of the road, but at the moment, I am happy with things.
"I am only 24, so the most important thing for me is to continue playing in the Sunderland first team and gain more experience, which is possible here."
Mignolet has been ousted by Thibaut Courtois as the No.1 for the national side, but the keeper is determined to win back his place back in Marc Wilmots' star-studded line-up.
"Of course I want to become the first choice goalkeeper again.
"But the only thing I can do is to do my best week in, week out at Sunderland and then I guess it's up to the coach to decide. For now I am focused on my club."