Councillor Anthony Lowe said the market had been open for 800 years, and that various groups were working behind the scenes to make sure it remained a part of Wellington life for years to come.
But while both Wellington Council and Telford & Wrekin Council would do what they could to protect the market, Councillor Lowe said they would be unable to simply purchase it outright.
The indoor and outdoor market has been put up for sale, little more than 12 months after the company managing the site pledged to invest in its future.
The property is being listed with the estate agents Lambert Smith Hampton, and is described as a retail investment opportunity.
More than 120 pitches are included in the site that is up for sale, along with a cafe and piazza, and two sets of self-contained retail units, as well as residential accommodation above.
Councillor Lowe said: "It is impossible to imagine Wellington retail offer without the market.
"It's not going to be allowed to fail on our watch after 800 years.
"There are active discussions taking place between the town council and the Telford & Wrekin borough council through the Wellington Regeneration Board – I don't sit on that, but Wellington Market is top of their agenda.
"We are aware it is a difficult time for the traders, because of the uncertainty, but it if it is sold it could be a new beginning."
Councillor Lowe said that if it returned, it would need to be made more modern.
"It is going to have to be preconfigured as a market for the 21st century. That will involve capital investment, and the question is where that is going to come from.
"We are custodians of the public purse – we can't just buy the market. However, we can facilitate a plan to inject capital into the market.
"There are several examples of successful markets. Altrincham in Cheshire is a massive success story, and Shrewsbury Market is fabulous for the town.
"The demographic in Wellington is different, but that means the market offer needs to be different. There is everything to play for."