A new £8m state-of-the-art leisure centre should be built in Cromer rather than as a replacement for the Splash sports and swimming complex in Sheringham.
District councillor Simon Hester, who lives in Fakenham, suggested the idea at North Norfolk District Council's overview and scrutiny committee meeting on Wednesday.
But it was not endorsed by other members of the committee who suggested the council press ahead with its preferred plan to knock the centre down and rebuild it to improve leisure provision in the district.
Mr Hester said: 'I'm not against the scheme but my suggestion would be to build a site here in Cromer in Holt Road. The new roundabout is being built in Holt Road and the train station is nearby, which would bring people in. It's a good location.
'We could then maybe have a cinema and more retail outlets on the site. We could redevelop the Splash site in Sheringham for housing.'
Glyn Williams, vice-chairman of the committee, said he admired the ambition of the plan, but added: 'We need to be ambitious for the Sheringham site.'
The meeting was told that Splash was used by 160,000 people yearly, but was being subsidised by the council to the tune of 70p per user.
Council leader Tom FitzPatrick said replacing the existing wet facility in Sheringham was a brave decision as some towns were closing swimming pools because they were so expensive to run.
He said: 'For leisure and fitness reasons we've got to make good use of our assets.'
The final decision on the proposals will be made by Cabinet.
It was previously reported that a new hotel and retail development in Sheringham could fund the new state-of-the-art swimming pool in the town.
The council's preferred option for replacing the ageing Splash centre was revealed earlier this year. It could be paid for using a combination of long term loans, Sport England funding and income from additional development on neighbouring land.
It is unlikely any new building will be completed before the council's current leisure contract with Places for People, which also covers Fakenham Sports and Fitness, and Victory Swim and Fitness Centre in North Walsham, ends on March 31, 2019.
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