However, it said "a number of significant issues remain unresolved", and added there is no certainty that the discussions will result in a transaction.
Both companies confirmed the ongoing negotiations but declined to comment further.
In a statement on its website, Myllykoski said it has been in negotiations with its financiers on its debt.
It said: "The company has been engaged in negotiations with various partners regarding structural arrangements.
"Negotiations with UPM are ongoing and thus Myllykoski will not comment on this at this stage."
It is understood that Myllykoski holds a 14% share in the European magazine paper market, meaning that if the transaction went ahead, UPM would command a 35% market share in that sector.
Helsinki-based UPM has 23,000 staff and in 2009 recorded turnover of €7.7bn (£6.5bn).
Family-owned Myllykoski is an international paper manufacturer that produces uncoated and coated publication papers, including newsprint.
It operates seven paper mills with a total annual capacity of 3m tonnes, and employs 2,700 people.
Earlier this month, it was revealed that the European newsprint market could be on the verge of a massive shake-up following reports that Stora Enso, Holmen and Norske Skog have been discussing a possible merger.
In 2008, newsprint manufacturer UPM said it had not ruled out consolidation, following rumours earlier in the year that UPM could merge with Stora Enso.
