Almost 800 postal workers in Merseyside are continuing their unofficial industrial despite reports of a national deal being brokered.
The Liverpool action is in a dispute over shift patterns
The Communication Workers' Union (CWU) claimed a total of 21 sorting offices were affected across the area.
But union officials said they were hopeful a deal could be hammered out very quickly after a "mood change".
The Royal Mail said they hoped employees will return to work after further meetings on Tuesday.
Mike Yarwood, area delivery representative for the CWU, said progress was being made.
"It is the most promising day so far," he said. "The mood of local managers has changed.
"We can't call another meeting until we have the document to show our members. We are waiting for the documents."
After a mass meeting on Monday union members said they had not heard sufficient detail on the national deal to convince them to return to work.
The Merseyside branch secretary for the CWU, Mark Walsh, has apologised to customers but said management is also to blame.
"I think Royal Mail have some responsibility. Our members want to deliver the mail and they want to get back to work to clear that backlog," he said.
"The sooner we can do that the better so we need a compromise to be reached."
Mr Yarwood said that once the document had been shown to postal workers, a deal could be struck in "three minutes" but they had to wait until after the executive committee meeting took place on Tuesday morning.
Postal workers in Liverpool started their unofficial action last Wednesday over a change in shift patterns.
The CWU national executive is due to meet later to consider the deal that was thrashed out between the Royal Mail officials and senior union officials on Friday night.
The executive will then decide whether to approve it and recommend it to the union's 130,000 members.