The KwikFit founder said closing the leisure pool at a time when the Olympics had increased interest in sport would be a great loss.
He urged the council to work with campaign group Splashback to find a future for the pool.
Sir Tom is one of the highest profile figures to back the campaign to reopen the pool, which has also enjoyed support in the past from author Irvine Welsh and the Proclaimers.
Sir Tom said: “With the success of our athletes during the Olympics and the Paralympics there is increased demand for sports facilities and it would be a great loss at this time and for future generations to lose all that Leith Waterworld has to offer.
“Whilst acknowledging the operational and financial cost of this facility, I urge the council to look closely at finding a way forward by working with Splashback to ensure that this community project is successful in retaining an important community swimming pool.”
A report by officials had recommended that tomorrow’s council meeting should throw out the rescue proposals and put the site on the market.
But the city’s ruling Labour-SNP coalition now plans to continue discussions with the group to see if an improved bid can be worked out.
Consultants have said the site should not be remarketed until February and now the administration wants to use that time to allow a revised community bid to be developed.
Councillors at tomorrow’s meeting are expected to be asked to formally reject the current bid, but agree to work with Splashback over the next four months on a revised plan.
Deputy council leader Steve Cardownie, who leads the SNP group, said: “The original decision to close Leith Waterworld was made in 2005 by the then Labour administration with all party support.
“Since the building is going to be mothballed until it is marketed again, it does make sense to continue discussions with Splashback to see if their bid can be developed.
“It would seem churlish not to use the four-month window of opportunity, but the marker is down that if the bid is not acceptable by then, we will proceed with the sale.”