There are “genuine grounds for hope” that at least parts of Wilko will be taken over, according to the GMB union.
National secretary Andy Prendergast said he had met PwC, the firm overseeing the sale of the retailer.
He confirmed there had been expressions of interest in the business, adding that talks with potential buyers were “still at an early stage”.
Wilko announced last week that it was going into administration, putting 12,500 jobs at risk.
“We can confirm there have been expressions of interest from organisations who are considering taking over at least some parts of the business,” Mr Prendergast said.
“These are still at an early stage, but means there are genuine grounds for hope.”
At the moment, all 400 Wilko shops remain open and staff continue to be paid in full.
However, it is unlikely that all the shops will be saved and thousands of workers are facing the threat of redundancy.
Wilko also employs people at its head office in Worksop in Nottinghamshire. In addition, it has distribution centres, in Worksop and Newport in Wales.
The chain is set to launch an “everything must go” sale on Friday but shelves will be replenished when new stock arrives at the beginning of next week.
It is not clear as yet which companies are bidding for Wilko.
There is speculation that rival discounters such as B&M and Poundland could be among possible buyers. Both firms declined to comment when contacted by the BBC on Thursday.
The Sun reported that The Range and Home Bargains could be among the bidders for Wilko. Home Bargains declined to comment and The Range did not respond to a request for comment.
Private equity firms Alteri and Gordon Brothers may be interested in investing in Wilko, according to reports.
Alteri declined to comment. Gordon Brothers did not respond to a request for comment.
PwC set a deadline of Wednesday to receive expressions of interest for Wilko, which has been trading since 1930.
Part of its task as administrator is to secure the best possible deal for the retailer’s creditors.
One of Wilko’s largest investors is Hilco, the specialist firm, which has provided millions of pounds in loans to the company.