The Millers are currently led by interim boss Paul Warne, who has been at the helm since November after Alan Stubbs and Kenny Jackett both left within the first three months of the season.
Warne has been unable to lead them away from danger and their relegation to Sky Bet League One could be confirmed in their first game after the international break.
Chairman Tony Stewart says they will make a decision on their new man after the local derby with Sheffield Wednesday on April 4.
"What we will do is make a statement about the direction in which we will be moving forward in preparation for next season," Stewart said. "The strategy will be revealed.
"Decisions will be made so people aren't left guessing after the Sheffield Wednesday game.
"We need to appoint a new manager before the end of the season. We're in the run-up to the end of this season. But we're also in the run-up to the start of next season.
"Any manager needs preparation. Our next manager needs to be doing it very soon. It's inevitable we are going to go down, but we are not a sinking ship. We're down, but we're not out."
On Warne, who has admitted he would take the job if offered, Stewart added: "Warney has got to be a candidate. He's got the culture of the club, he's got the knowledge.
"He will be competing with two or three others we have in mind."