Stewart, who is currently interviewing eight candidates for the vacant managerial post, has invited the Millers dressing room to help choose Mark Robins' successor.
Stewart, who has been involved in football under 18 months, wants to avoid an unpopular appointment after recalling events at Leeds 35 years ago after the late Brian Clough was handed the job.
Stewart told the Yorkshire Post: "We are allowing names to filter down to the team to get feedback.
"I think that it is a good idea because we don't want a situation that happened with Mr Clough at Leeds. It's important that there is respect and that people are motivated by the individual."