There are around 60 traders in the centre, in Sauchiehall Street, who had all been told to pack up their shops and leave the site by last Friday.
The shock came after InShops, the operator of the centre, announced it was going into liquidation.
However, talks got underway last week between the owner of the building, PBN Properties, and InShops.
Savoy retailers told the Evening Times that they were hopeful that a deal would be struck, and that officials were due to discuss the terms with them in the coming days.
It is understood some traders had meetings with the landlords yesterday, with the other meetings due to take place next week.
The news has given the small companies renewed hope for the future of the closure-threatened indoor market.
The centre has been operating in Glasgow for more than 30 years and includes cafes, interior shops and beauty salons.
Dougie Fraser and his mum Yvonne Elliot, from Newton Mearns, have owned print firm Image Box in the Savoy for just over a year.
Mr Fraser, 24. said he was hopeful that new management would result in the entire site being refreshed.
He said: "I would like to see some of the units filled up, it's been empty for too long. It is in a great location - we're in the middle of Sauchiehall Street - but we need to get more people into the centre.
"If they just put a bit of work into it, to make the signage better, to advertise us more and brighten it up, then we would be busier."
Ms Elliot, 57, added: "We've already seen former tenants come and have a look at the sites since they found out that it was going to have new operators."
Gordon Barr, 48, has been owner of watch repair firm Tick Tock for 25 years.
He said: "It would be good to see the Savoy back to its best. It doesn't even need that much - just a general spruce up and tidy up.
"We really need to be advertised more, too, so more people come in and have a look. There are a lot of good services here."
George Roger, 37, who runs shoe repair business Mac's with his brother Stewart, said the key was to make sure the vacant spaces in the centre were occupied.
He said: "We need to get more people into the centre.
"But they need to improve the centre and give the traders the support they need."
A creditors' meeting which was organised by accountancy firm KPMG was held in Manchester on Tuesday in a bid to appoint liquidators.
However, it is understood to be too early for an official announcement.
InShops ran around 50 centres across the country.