Championship Rotherham have confirmed they have asked for permission to speak with Stubbs, and have been waiting over the weekend for the Scottish side to deliver their verdict.
They have also approached another club, believed to be League One Coventry City, with Sky Blues boss Tony Mowbray also said to be in the frame.
But The Star understands that Stubbs is the man they want most.
His odds have dropped to 1/10 in the betting market, with Mowbray at 5/1.
Hibs have been doing no business this weekend, but their chief executive, Leean Dempster, is likely to be speaking with Stubbs to gauge the level of his interest in the vacant hot-seat at AESSEAL New York Stadium.
Stewart, keen to see Rotherham move up the table after two seasons of survival struggle in the Championship, believes he can land either manager as long as their clubs give the green light for dialogue to begin.
“It’s all about moving forward,” he said. “I think if we get permission, the rest would be plain sailing.”
Stubbs - like Mowbray - has a year left on his contracts and compensation would be due to Hibs if they give their consent for talks and the 44-year-old accepted the Millers job.
After interviewing four out-of-work candidates, Rotherham decided to extend their search for a successor to Neil Warnock and Stewart was true to his word that they were ready to try to lure a manager already in a job to New York.
The Millers went through the proper channels on Friday, making official contact with both clubs.
“There are certain protocols and we have always adhered to them,” Stewart said. “There is a right way of doing things. We don’t speak to anyone without permission. I wouldn’t like that to be done to me, so we don’t do it to them.”
If progress is relatively smooth, he says the Millers could be in a position to make an announcement on or around Wednesday.
Whoever takes the job, they have a tough act to follow after the departure of Warnock who inspired an 11-match unbeaten run during his three-month reign to keep the Rotherham in the second tier.
Stubbs, in charge at Easter Road for the last two seasons, was close to landing the Millers post when it went to Neil Redfearn last October.
Meanwhile, Rotherham will play a pre-season friendly against Parkgate FC at Roundwood on Saturday July 9 (KO noon).