The unit occupied by Beccles' HSBC branch could become an "independent business" that would benefit young people after the bank leaves the town.
Waveney MP Peter Aldous said he had a "positive conversation" with the owners of the building on New Market about its future, after HSBC's planned closure on June 27.
Speaking at a town council meeting on Tuesday night, Mr Aldous said: "The building owners share our disappointment that HSBC will not be renewing the lease.
"Ideally, they would like the property to be re-let as soon as possible when the bank leaves in June, but they will wait for the 'right tenant'.
"Their preference is to let to an independent business, and in some way, they hope the space can benefit young people in the town.
"My correspondence with the building owners was very positive and fell neatly within the lines of what we hoped best for the future of the building."
The Beccles branch is one of 144 plans to close across the country this year.
Mr Aldous and the town council are concerned this will lead to extra pressure on the Post Office, with councillors already deeming it "unfit" in its current state.
The council heard that the Post Office has not yet responded to Mr Aldous since he wrote to them in December.
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Mr Aldous also warned he has "seen the bank dominos fall" in neighbouring towns, and hopes to prevent another market town from being left bankless.
To seek reassurance from the town's two remaining banks, Barclays and Lloyds, councillors voted unanimously to request Mr Aldous, on behalf of the town, to write to the banks to seek their vision and commitment to the town.
Councillor Graham Catchpole said Mr Aldous should write to them because the council would only get a "generic response" from the banks.
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