HITC Sport understands Stoke are aiming to win the race for Sunderland midfielder.
McNair's future at Sunderland has been the subject of conjecture this summer with Brighton and Middlesbrough chasing his signature.
Brighton saw two bids for the Northern Ireland international rejected earlier this summer, while Middlesbrough agreed a fee in the region of £5million for McNair this month.
However, Stoke have now entered the race for McNair with Potters boss Gary Rowett keen to bring the versatile performer to the club.
Sunderland are reluctant to lose McNair, but accept they need to sell players to raise funds for their own transfer plans following their relegation from the Championship last season.
McNair was one of Sunderland's shining lights last season despite their disappointing campaign, chipping in with five goals in 18 appearances for the Black Cats.
The former Manchester United youngster's form at the back end of the season has prompted the interest from Brighton and Middlesbrough, but Stoke are hoping to win the race for his services.
Rowett is keen to build a side capable of winning promotion back to the Premier League at the first time of asking and sees McNair as a key addition to his plans.
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