Rangers are on the lookout for a new permanent manager following the departure of Pedro Caixinha due to a run of disappointing results in the Scottish Premiership.
According to The Sunday Post, Rangers are set to announce McInnes as their new manager this week.
It has been reported that the Gers have the finance to meet the £800,000 compensation payment to secure the services of McInnes and his assistant Tony Docherty.
Mackay-Steven joined Aberdeen from Celtic in the summer transfer window and has been playing well so far this season.
The 27-year-old Scotland international winger has suggested that he and his teammates are not taking much notice of speculation linking McInnes with a move to Rangers.
The former Airdrie United and Dundee United star has also stated that he and his Aberdeen teammates want the ex-Rangers midfielder to remain at the Pittodrie Stadium.
“I don’t think the talk has had an impact at all,” Mackay-Steven told The Scottish Sun. “As far as the dressing room is concerned, it’s all speculation.
“I don’t think it’s affected us one bit. Until someone tells us otherwise, we’ll go about our business as usual.
“We want the manager to stay at Pittodrie, definitely. I think I speak for all the boys when I say we want him to stay.
“You look at what he’s done for Aberdeen. He is a great manager. It’s just speculation, so we’ll keep doing what we do.”