Rangers had an approach for the 46-year-old dismissed out of hand by their rivals on Tuesday evening.
Dave King and his board are still determined to land McInnes and will be expected to make a second approach in the coming days.
However, Aberdeen chief Stewart Milne is determined to hold on to his man and will meet McInnes on Wednesday afternoon to discuss the situation.
It is believed that McInnes would wish to speak with representatives from Rangers about the possibility of him taking over as the successor to Pedro Caixinha.
In order to do so, he may have to rip up his contract with the Pittodrie club, unless he and Milne can come to some sort of agreement.
It has also been reported by the BBC that McInnes will not take charge of Aberdeen’s training session on Wednesday morning.