The open air market and car boot sale in the Common Haugh car park has been trading in the town for more than 40 years.
But there has been a noticeable decline in both stallholders and visitors in more recent times.
It was operated by Geraud UK, part of the French company Groupe Geraud, from 2015 but its £5,000-a-year contract expired last September.
Yesterday, Tuesday, March 16, members of the town's common good fund sub-committee were informed that three options were now being considered for its future.
Those included seeking a new operator or existing stallholder to take it over, to carry out a feasibility study on the possibility of different types of open air markets and to consider allowing a Third Sector community-based organisation to operate it, with potential support from South of Scotland Enterprise.
Hawick and Denholm councillor Clair Ramage favours the third option.
She said: "We have to think differently and we can't continue to live in the past. I know what it was like when I came to Hawick, it was massive and it was a great on a Saturday morning walking through the stalls.
"The third-sector community-based approach really appeals to me.
"Through lockdown people have picked up crafts and they are looking to get a pop-up shop on the high street and that's difficult. Here is an opportunity to be selling at the stalls."
Hawick and Hermitage's councillor Davie Patterson said there was one stallholder who had expressed a strong interest in taking over and also claimed "the market died" when the French company took it over in 2015.
He added: "I speak to this stallholder every week and he tells me he has tried to contact officers and they've not got back to him, this guy want to take over the market and build it up.
"I don't want the market to die and I think we can rejuvenate it. It's money for the common good fund, money we can use within the town. We can still look at the other options if there are grants available."
Town provost Watson McAteer added: "I'm really interested in that community-led approach and whether there would be an appetite for that and if that is worth exploring.
"Given where we are in giving communities more opportunities to be empowered, to spend money where they want to spend it, it seems logical that that sort of approach would be something someone would be interested in.
"The market has not been working and so we have to think differently, even if that means using different locations. We need to be agile and think on our feet.”