The Rangers targets appear to be edging closer to a move to Ibrox.
Aberdeen confirmed in a statement they had blocked an attempt from Rangers to appoint McInnes as manager.
The latter publication added that McInnes could be forced to hand in his resignation if Aberdeen continue to play hardball.
And the former Gers midfielder's alleged absence from training would appear to suggest his wish is close to being granted.
According to the Scottish Sun, Rangers' planned offer could exceed the £1 million mark, as they persist with trying to land their 'number 1 target' following Pedro Caixinha's sacking six weeks ago on Thursday.
The Paisley-born boss saw his side overtaken by Rangers at the weekend, after back-to-back defeats to the 54-time Scottish champions in the space of a week.