Paul Warne is leaving the club to take over at Derby County.
It is believed that Warne will leave after six years in charge.
Since taking over in November 2016 the 49-year-old has led the Millers to promotion to the Championship three times.
He had two spells with the club as a player.
After Wayne Rooney decided to quit after the Rams' promotion to League One, Rosenior was relieved of his duties.
The Millers sit in eighth place with 14 points from their first nine games.
He took over at the New York Stadium after Kenny Jackett's short spell in charge.
The club's fitness coach was unable to keep them up in the second tier but he was able to get them back to the second tier through the play-offs.
The League One season was shortened due to the coronaviruses and they were promoted to second place in the season that ended in March.
On the final day of the 2020-21 season, they were once again condemned to be in the bottom half of the table, but once again, they were led back up by Warne.
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