Wilko - which has stores in Ammanford, Llanelli and Carmarthen - has suspended redundancies while administrators consider rescue offers, according to the GMB union.
The union, which represents more than 3,000 of Wilko’s 12,500 staff, said it met with administrators on Tuesday morning.
Wilko tumbled into administration earlier this month, putting the future of its 400 stores across the UK into doubt.
Administrators from PwC have sought offers from interested firms in an effort to save jobs and stores.
The union said on Tuesday it discussed a number of potential bids to save the stricken high street chain with the insolvency experts.
Andy Prendergast, GMB national secretary, said: “All redundancies at Wilko have been suspended while the administrator considers further bids.
“Whilst this is a positive development, Wilko is not out of the woods by any means and this is a time of incredible stress and worry for the 12,500 workers who face losing their jobs.”
It comes after reports of fresh last-minute bids to potentially buy the retailer.
A bid worth £90 million has been made by restructuring specialist M2 Capital, the Guardian reported, which could potentially keep the entire Wilko chain trading.
It came after Canadian businessman Doug Putman, who bought music retailer HMV in 2019, also lodged a bid intended to preserve the majority of Wilko’s stores.
Rivals Poundland, B&M, The Range and Home Bargains also reportedly lodged their interest in buying parts of the Wilko business.
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here