The Millers are in the box seat to sign the striker, who hit 17 goals for the Grecians last term.
Rotherham chief and former Exeter manager Matt Taylor brought Nombe to Exeter from MK Dons in the summer of 2021.
Yorkshire rivals Barnsley had been also keen on Nombe, but he is now destined for elsewhere. Late last week, Birmingham and Wrexham were also reportedly credited with interest.
Speaking after Exeter's EFL Cup tie with Stevenage on Tuesday night, Caldwell confirmed ‘a couple of bids’ have been accepted.
“Sam is speaking with other clubs and we will have to wait to see what develops,” he said.
“There is no definitive movement yet. He is talking with other clubs and we have accepted a couple of bids and I am sure there will be more information on that tomorrow (Wednesday)."
The Millers chief has targeted three signings in the final week of the window, while some fringe players could also leave the club.
Striker Josh Kayode is a target for Barnsley, but there is rival lower-division interest.
Speaking about his transfer plans after Saturday’s game with Leicester, Taylor said: "It's a big week for us. We can't hide away from that fact.
"I think there will be players going out, potentially on loan, potentially on permanent deals.
"We're trying to free up some funds and we're going to be as aggressive as the team played on Saturday: get on the front foot and put our best offers to people. We'll see where it takes us.
"I'd love to have three more bodies in before the Norwich game.”