Cotterill said after the Capital One Cup defeat at Luton on Tuesday night that the Robins’ offer, believed to be £6million, had been accepted by the Eagles.
Gayle, who joined Palace from Peterborough in the summer of 2013, scored 10 goals in 29 appearances last season, but does not appear to be in Alan Pardew’s plans following the arrivals of Patrick Bamford and Connor Wickham at Selhurst Park.
Yet it remains to be seen whether Gayle is willing to drop down to the Sky Bet Championship and Cotterill says the 24-year-old has until the end of the week to decide whether he wants to join Bristol City.
“We are no further down the line with that one (Gayle) than we were on Tuesday,” Cotterill said ahead of Saturday’s home league game against Brentford.
“There have been a couple of conversations, not face-to-face, and we are not any further advanced.
“We are on a timescale with this one and we will not be on it forever. It’s really getting to crunch time this week with that one.”
Cotterill also admitted on Bristol City Player: “It all boils down to the fact the lad wants to think about it.
“The only thing that’s happened since Tuesday is the couple of phone calls and I wouldn’t say that is good progression (for the transfer).
“If the lad wants to stay (at Palace) then fine and good luck to him.
“We just can’t wait around forever, we need a decision.”