The Millers are looking for a third boss of the season and sixth in 14 months after Kenny Jackett surprisingly quit on Monday after only five games and 39 days in charge.
Several reports north of the border said that they tried to hijack MK Dons’ approach for the 36-year-old, but the South Yorkshire club insist that is not true.
A club statement read: “Following media reports this morning, Rotherham United can confirm that the club has not sought or made any approach to Heart of Midlothian FC for manager Robbie Neilson.”
Neilson, who reportedly travelled south for talks with the League One Dons earlier this week, could be set to take charge of his final game as Hearts manager against Rangers on Wednesday night.
Meanwhile, Millers chairman Tony Stewart finds himself in the all-too familiar position of trying to find a new manager.
Stewart has appointed Neil Redfearn, Neil Warnock, Alan Stubbs and Jackett in the last 13 months, but will not rush this appointment.
His club are 11 points adrift of safety in the Championship, without a win in 14, and are almost certainly going to be in League One next season.
“I think we have to think long and hard,” Stewart said. “When you look at the successful managers we have had in the past, they had the combination of enthusiasm and passion, coupled with the skill to get the best out of the playing staff. Those are the characteristics we are looking for.
“Paul Warne has agreed to take charge of first-team matters in the interim, and we are pleased to have someone like him, a committed Miller, in caretaker control.
“This is now another challenge. I welcome challenges, and I remain positive that we will find someone who can take this club forward. And I mean take this club forward.
“As you would expect, we have already had a number of enquiries but what we want to try and avoid is rushing what will be a very important appointment for the football club.”