The allegation -- formally denied by Temer in a statement from the president's office -- was reportedly made by Claudio Melo Filho, a jailed former senior Odebrecht executive, as part of a plea deal for a lighter sentence.
The allegation threatens to destabilize Temer's presidency just six months after he took office seeking to rescue Latin America's biggest economy from crisis.
"President Michel Temer vehemently rejects the false accusations of Melo Filho," the statement read. "The donations made by the Odebrecht group to the PMDB (Temer's center-right party) were all made through bank transfers" declared to the election authorities.
Melo Filho is one of the 77 construction giant's current and former executives that have signed plea deals and agreed to cooperate with prosecutors in return for lighter sentences, a source close to Odebrecht told AFP earlier.
Details of the plea deals have been emerging in information leaked to the press.
The 77 include the firm's jailed boss Marcelo Odebrecht, who was reported earlier this year to have named Temer in testimony to investigators. Odebrecht received a 19-year jail sentence in 2015 for corruption and money-laundering.
Melo Filho said the money his company gave Temer was partly used to finance the campaign of Paulo Skaf, a PMDB candidate for governor of the state of Sao Pablo in 2014.
The plea deals could lead to some 130 more suspects -- including many elected officials -- being dragged into the sprawling probe of the Petrobras state-owned oil company, dubbed Operation Car Wash by investigators, Brazilian media said.
Prosecutors believe Petrobras was systematically plundered by a network of executives, politicians and contractors such as Odebrecht.
Temer took office in late August after the elected leftist president, Dilma Rousseff, was impeached on charges of moving money between government accounts for political purposes.