Mignolet was shown around the Stadium of Light and the club's training ground at the weekend as Sunderland looked to fend off competition from PSV Eindhoven for the 21-year-old.
Vaesen claims his client has agreed a five-year deal with the Black Cats, who must now agree a fee with Mignolet's current club St Truidense.
"Simon has made a choice that he wants to sign for Sunderland and it is now up to the clubs to find an agreement as quickly as possible," Vaesen told The Journal.
"He did have options but he has decided to go to Sunderland. It is still to be finalised but I think it is close now, the clubs are not far apart on a fee. I think we're 99% agreed on everything and there are no problems."
Mignolet will act as back up to Sunderland number one Craig Gordon with Marton Fulop expected to leave the club over the summer.