The English Championship side are on the hunt for a new manager following Neil Warnock’s departure at the end of the season.
They are expected to contact Hibs and make an official approach for Stubbs.
Warnock kept Rotherham up, with the Millers finishing in 21st place in the second tier.
Their chairman Tony Stewart told STV: “Alan Stubbs is one of our three favourites for the job but we will do things the right way. We must first ask Hibs for permission before we speak to Alan directly.”
Stubbs’ guided Hibs to a remarkable Scottish Cup final triumph over Rangers last weekend and his stock his high despite the Edinburgh club’s failure to win promotion to the Premiership for the second season running.
Rotherham would certainly be able to offer higher wages but Stubbs may be reluctant to walk away from Hibs after the success of last weekend and the opportunity to play in Europe next season. He has a year remaining on his Easter Road contract.
Rotherham chairman Stewart added: “Since being promoted to the Championship we have twice narrowly avoided relegation but we have learned very little from the experience. We want a manager who can help the club grow and take us up the league.”
Rotherham are also understood to be interested in Tony Mowbray, the former Hibs manager currently in charge of Coventry, and Owen Coyle, who this week parted company with Houston Dynamo.