The Northern Ireland international is approaching the end of a deal which has already been extended once, but United will attempt to keep him at Elland Road beyond their clash with Cardiff City, the last match of his loan.
McCartney came to Leeds towards the end of September and was due to return this weekend, but Sunderland agreed to increase his month-long stay by an extra two days to encompass Monday's clash, originally scheduled for tomorrow.
The 29-year-old left-back has played in all five of United's fixtures during his time in Yorkshire with Federico Bessone and Ben Parker injured, and his steady performances have convinced Grayson to press for a fresh agreement in the aftermath of the Cardiff match.
McCartney is not part of Bruce's plans at the Stadium of Light and was not given a squad number by the Premier League club at the start of the season.
Grayson said: "I've been delighted with him. He's shown the qualities that made him the Premier League player he is and worth the money he's gone for in the past.
"He'll get better with more time on the pitch. You always want to keep good players and I've spoken to Steve. If there's a deal to be done then he's somebody I'd like to keep."
Bessone is fit again after a knock sustained last month but Parker, who damaged an Achilles tendon in April, is not yet ready for a first-team return, despite completing 90 minutes in a friendly against Stoke City on Wednesday.