The Millers are waiting to see whether Taylor accepts the position to take over from Paul Warne, with the 40-year-old set to decide imminently.
Both Rotherham and Exeter confirmed on Saturday night that talks had taken place and Taylor has been offered the job.
Taylor, who took the reins at St James’ Park in 2018, went on record about it after the Grecians’ 2-2 draw with Bristol Rovers, saying that he has some soul-searching to do.
Exeter City manager Matt Taylor has been approached to take over as boss of Rotherham United. (Photo by Pete Norton/Getty Images)
“I have a decision to make and I’ll be making that decision within the next 24 hours,” he said.
“I have been approached and that’s all I can say – I have a decision to make.
“You have to move every now and then and you have to keep looking forward.
“I can’t say I have decided either way, but I have to make a decision. It comes down to family, the personnel I speak to every day in the changing room and the staff I speak to every day.
“It’d be a huge wrench to leave, absolutely massive. I have given 10 years of service to the football club, four as a player, one and three quarter years as a coach and then three and a quarter years as a manager, so I have certainly done a lot for this club and I am incredibly proud of what I have achieved alongside a lot of people.”
The Millers turned their attention to Taylor after missing out on Cambridge boss Mark Bonner earlier this week, with the 36-year-old opting to stay with his boyhood club.
They lost their first game without warning as they went down to a 2-0 home defeat to Wigan on Saturday.
The side were led by club captain Richard Wood and senior player Lee Peltier, though the pair now look unlikely to be in charge for Wednesday’s visit of Millwall.
Wood said he would continue to take the team for as long as is necessary, but the Millers hope to be able to unveil Taylor before then.
Following Saturday’s defeat, the stand-in boss said: “I am very disappointed with how we turned out and performed because it wasn’t us. It just wasn’t there.
“People underperformed and we were just not at the races.
“Preparation this week has been very good. The tempo in training has been very good. We were as prepared as we have always been.
“I don’t know if emotionally it took a toll on certain players. When so many underperform you are never going to win a game. It’s a big thing that has happened, losing the manager of six years.
“We didn’t start well. We were like rabbits in headlights. We will see where we went wrong on Monday.
“I have loved this week. I did not realize how much work goes into it behind the scenes. I have grown into it during the week.
“I will do it for as long as possible and see what happens but I have no idea what is going on behind the scenes.”
