Aberdeen's chairman Stewart Milne made a statement on the issue: "I spoke with Derek who felt it was a major thing to be considered for the managerial position at a club such as Rangers and we agreed that he could have some time to think about the approach and talk it through with his family."
McInnes has enjoyed some good success at Aberdeen, winning the League Cup in 2014. It was the first time the club won a trophy in 19 years. Aberdeen also reached the final of both Scottish cup competitions last season.
Chairman Milne added: "Over the past 48 hours, I have been in constant dialogue with Derek and having weighed up the opportunity, he has taken the decision to remain as Aberdeen FC manager. Derek has also been maintaining close contact with Paul Sheerin ahead of tomorrow's game at Dundee.
McInnes also spoke about the situation: "I've had a lot to consider over the last couple of days and I appreciate it's been a testing time for everyone, including my family, and I'm pleased to be now totally focusing on purely on on-the-field matters."