The retailers were told to pack up their shops, cafes and food outlets a week ago and leave the premises by today.
However, it is under-stood that talks were expected to continue into next week in a bid to keep the businesses open.
The traders had received the shock news through a letter from shopping centre operator InShops, which said it was going into liquidation.
The centre, in Sauchiehall Street, and the office block above it is owned by Belfast-based group PBN Properties.
An inside source said: "Discussions are ongoing and everyone is hopeful that there will be a positive outcome. Traders are opening as normal. Liquidators are due to be appointed during next week."
A meeting of cred-itors has been organ-ised by accountancy firm KPMG for Tuesday in Manchester.
There are more than 60 small businesses, including hardware shops, cafes and furniture stores in the centre, which has a weekly footfall of al-most 50,000 customers.
The plight of the traders in the market, known for providing affordable products, was raised in the Scottish Parliament.
Glasgow Kelvin SNP MSP, Sandra White, asked Deputy First Minister Nicola Sturgeon what support the Scottish Govern-ment could offer and asked if she would meet with the traders.
Ms Sturgeon said she was aware of the situation and saddened by the potential closure.
She said: "We have been in contact with KPMG who are in discussions with InShops and I have been asked to be kept informed."
In the letter received by the traders on January 10, InShops chief executive Frederic Bonnet said: "Traders and sub-tenants need to vacate the sites prior to the close of business on January 17."
He added that InShops Centre Limited and In-Shops Starters Limited had, "suffered from increas-ing losses and are now unable to generate sufficient cash to allow them to continue".
He wrote that the firm had been working with advisers to find a solution but despite this, the directors "have concluded that the business can no longer continue to trade".
Shopping develop-ments run by the company across the UK have been affected.