Rangers were reportedly keen on the Wolves midfielder, but opted to bring Barton to Ibrox instead.
The midfielder looks set to depart Wolverhampton Wanderers this summer after falling out of favour at the end of last season.
He failed to make an appearance after March for Kenny Jacket’s side as the Wolves boss preferred other options ahead of him.
Rangers were one of the team interested in his signature, with the Express & Star reporting that Gers boss Mark Warburton was keen on his signature.
However, according to the Mirror, that potential deal fell through as they instead made a move to secure Barton with his contract expiring at Burnley.
Warburton was keen to add experience to his squad this summer and it is likely he felt Barton, who was one of the star men in the Championship last season, would be the better choice.
It now remains to be seen where McDonald will end up, with an exit from Molineux looking increasingly likely. The same report from the Mirror reports that he is currently closing in on a move to Fulham.