According to Bloomberg, the merger would require both press manufacturers to shed some assets where businesses overlap and by doing so, this would help gain much-needed backing from the antitrust authorities.
Otherwise, the merger would result in a body that has a 65% market share of the press sector.
The latest speculation follows German trade media reports in Manager Magazin, which claimed that Heidelberg and Manroland had appointed Merrill Lynch and Deutsche Bank respectively to advise on the potential merger.
The title reinforced the latest claims reporting that the new company would need to dispose of the Manroland sheetfed manufacturing site in Offenbach, which currently employs 2,500 people.
Rumours of a merger between the press manufacturers come at a time when Heidelberg warned that it did not expect to make a profit in the current 2009/10 financial year.
This followed on from the publication of its first-quarter results in which it posted a €63m (£54.2m) operating loss.