McInnes is the man the Glasgow giants want to replace Pedro Caixinha in charge.
After dragging their feet for six weeks they finally made an official approach earlier this week.
However Aberdeen chairman Stewart Milne publicly shot Rangers down, denying them permission to speak to his manager.
McInnes held talks with Milne yesterday but failed to change his mind about letting him go.
But if there is to be a chance of mindset from the Pittodrie top man, Starsport understands a switch to Ibrox could be wrapped up quickly.
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A three-year deal would be on offer to McInnes and the contract would be quickly thrashed out.
Rangers host Ross County on Saturday and if Aberdeen decide to let him go before then he could feasibly be at the game.
The Dons travel to Dundee tomorrow night and it’s unlikely McInnes will take charge.
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He and assistant Tony Docherty skipped training yesterday with Paul Sheerin and Barry Robson taking the session instead.
The youth team coaches could step into the dugout tomorrow if a switch to Rangers for McInnes draws closer.
McInnes was appointed Aberdeen manager in 2013 and has steered the club to three consecutive second-place finishes in the Scottish top flight.