Hartlepool have announced they will not sign convicted rapist Ched Evans after boss Ronnie Moore expressed an interest.
Arsenal manager Arsene Wenger insists he will only spend money in January on the right player.
Mignolet's representative, Guy Vandersmissen told the Belgian media the keeper may need a bigger stage in order to gain international recognition.
The 24-year-old is currently understudy in the Belgium squad to Chelsea's Thibaut Courtois - who is spending his second season on-loan at Athletico Madrid.
"Our ambition is for Simon to play somewhere that he can engage in competition with Thibaut Courtois for the place in goal for Belgium," said Vandersmissen.
"Courtois is fortunate that he is playing for a team that has been doing well lately."
Mignolet still has a further two years to run on his Sunderland contract, and there were tentative discussions over a new deal earlier this season.
And the stopper has made an impression with his form for Sunderland, after he was voted North East Football Writers' Player of the Year on Sunday.