At the time of writing, Heidelberg's shares were valued at €4.87, equal to a market value of €380m (£328m).
News of the talks stem from an announcement in the Platow Brief, a German financial newsletter, according to Bloomberg.
The newsletter reports that German insurance company Allianz, which has a 65% stake in Manroland and a 12% stake in Heidelberg, is keen on the merger.
Last week, Heidelberg revealed incoming orders had dropped 20% to €2.91bn (£2.5bn).
Chief executive Bernhard Schreier told shareholders at its AGM that the past financial year had been "without doubt one of the worst in the more than 150-year history of Heidelberg - if not the worst".
George Clarke, managing director of Heidelberg UK, said the company "did not comment on market rumours". Manroland also returned a "no comment" regarding the rumours.
Heidelberg in merger talks with Manroland, according to German reports
Heidelberg's share price rose more than 5% yesterday (27 July), the highest in six weeks, following reports it is locked in talks with rival Manroland over a possible merger.
