Writing on Twitter on Sunday, Lynch said the network wasn't willing to pony up the money needed to make the show the way he wants, but said production may take place without him.
A similar statement attributed to Lynch was posted on the Twin Peaks Festival's Facebook page.
However, Showtime indicated it was still trying to work out a deal with Lynch.
“We were saddened to read David Lynch’s statement today since we believed we were working towards solutions with David and his reps on the few remaining deal points,” Showtime said in a statement cited by Variety. “Showtime also loves the world of ‘Twin Peaks’ and we continue to hold out hope that we can bring it back in all its glory with both of its extraordinary creators, David Lynch and Mark Frost, at its helm.”
According to Variety, Lynch and Frost had already written the nine episodes expected to air next year. Original "Twin Peaks" star Kyle MacLachlan said in January he would return as Special Agent Dale Cooper.
Sheryl Lee, who played Laura Palmer, and Dana Ashbrook, who played Laura's boyfriend Bobby, have both said they would be returning to the series as well.
However, Lynch indicated last month that there were some problems and that the reboot was "still up in the air."
"Twin Peaks" originally aired on ABC from 1990-1991, followed by the 1992 film "Twin Peaks: Fire Walk with Me."