The two parties met last week for the first time in almost three months, when a Unite party headed by general secretary Len McCluskey went to Austria to meet with the company's management.
Unite is in the process of taking legal action against MMP over the planned closure of its Bootle plant, which followed on-site protests over redundancy pay and terms.
According to Unite, the meeting came about when the company's chief executive personally called McCluskey, following increased pressure from a number of major customers.
MMP did confirm that this was the reason the meeting was set up, but a statement from the company said: "We confirm that a meeting took place last week in which the parties exchanged their views. Based on this it has been agreed to meet again soon."
It is unclear at this stage whether MMP intends to reopen the plant, but Unite assistant general secretary Tony Burke told PrintWeek that the union would not "collapse and go away" on the issue.
He said: "A number of their blue-chip customers feel very uncomfortable being connected with what is going on here and we have been pressing them to raise this issue with MMP, which they have done.
"As far as we are concerned, this dispute is still ongoing and we are continuing with action against the company. We have a strategy in place to take us well into 2013; we will not let our members be treated like this."
