McNair made 18 appearances for the 'Black Cats' as they were relegated from the Championship this season.
However, Brighton are keen to capitalise on Sunderland's misfortunes by luring the 23-year-old to the Amex Stadium.
If they are to succeed though, they will have to pay more than £2million after the now-League One club reportedly rejected their first offer.
McNair already has experience in the Premier League during his time at Manchester United, where he made 24 league appearances during the course of two seasons.
He has also been capped at international level for Northern Ireland, featuring 17 times so far.