Councillors will decide whether to accept a £1 million bid from a soft play firm to buy Leith Waterworld next Thursday.
City council leader Andrew Burns said the offer was being treated as “serious” and that councillors would vote on whether to accept it at next week’s full council meeting.
He said the local authority had not been actively marketing the site in recent months, with the unnamed interested firm’s approach unsolicited.
“It has come as a bit of a surprise,” Councillor Burns said.
Campaign group Splashback, which was given the green light to pursue a relaunch of the closed pool in January, called on councillors to reject the new bid.
A spokesperson said: “We believe that the conviction displayed by councillors on that day will guide their decision [next Thursday]. We look forward to continuing to work with the council to deliver on the commitments they made.”