The Lynn branch of LA Fitness is one of 33 of its gyms being sold across the UK.
The move is part of a wider restructure the company says it is undertaking to improve the gym facilities they are continuing to run.
A spokesman said the company is in talks around transferring ownership over to a competitor.
At this stage LAS Fitness will not name any interested parties but confirmed several companies have come forward. If the gym is not sold on then it would close.
The company is unable to provide information about a decision date.