It emerged over the weekend that Tony Pulis' side had lodged a bid, thought to be in excess of £5m for the Northern Ireland international.
That offer has now been accepted, leaving Boro in pole position to land the versatile former Manchester United star.
Pulis quickly identified midfield as an area he would like to strengthen after taking over form Garry Monk in December, initially bringing in Mo Besic on loan from Everton.
However, with Besic having now returned to his parent club he has now set his sights on a more permanent option, with McNair seen as the perfect man for the job.
McNair impressed for the 'Black Cats' last season, scoring five goals from midfield in what was an instantly forgettable campaign for all concerned with the club.
The 23-year-old made his desire to play at a higher level than League One clear and despite interest from Premier League side Brighton, who previously had two bids turned down, it now appears he will be starting afresh in the north east.