The South Yorkshire outfit had an initial offer rejected on the basis that it was to be paid up in instalments over two years.
Ton chairman Douglas Rae made clear that he would only accept a deal with the transfer fee paid up front, and the Tele understands that Rotherham have now returned with a second £50,000 bid.
Tidser and his agent will now meet with Millers officials at their New York Stadium tomorrow to try and thrash out personal terms and seal the move.
The 23-year-old told the Tele: "The chairman has accepted a bid from Rotherham.
"As far as I'm aware they came back in with an offer of the money up front.
"I found out yesterday and I'm going down tomorrow morning with my agent to see what they've got to say, maybe be shown about the place and try to agree terms.
"I was speaking to my mate Simon Ferry, who played with me at Celtic and was at Swindon for three years, and he said they're a great club, with a big stadium and a decent pitch.
"Nothing's set in stone yet so we'll just have to wait and see how things go tomorrow."