The Robins had placed a bid of around £8million for Gayle recently and Palace have gone on to accept the offer from the Championship side.
However, the move has not come to fruition as of yet as Gayle is stalling over his decision, prompting Bristol boss Cotterill to urge the striker to soon make up his mind.
Cotterill said: "We are no further down the line with that one (Gayle) than we were on Tuesday. 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. 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."