He was accused of authorising illicit payments to politician Eduardo Cunha, who was jailed in March for corruption, money laundering and tax evasion.
O Globo newspaper said it had obtained a recording of Mr Temer discussing the payments with a senior business leader.
Almost a third of the cabinet is under investigation for alleged corruption.
Mr Temer, a former law professor, played a key role in the impeachment proceedings against his predecessor, President Dilma Rousseff, last year.
As vice-president, he replaced her after she was impeached and removed from office.
O Globo says it has obtained recordings of a discussion between Mr Temer and an official from the giant meat-packing company JBS.
The newspaper says the tapes were presented in plea bargain negotiations between prosecutors and two JBS executives.
Michel Temer (left) is seen here with Eduardo Cunha in November 2015
Mr Temer's office says the allegations are false and is calling for them to be thoroughly investigated.
"President Michel Temer has never requested payments to obtain the silence of former MP Eduardo Cunha," it said.
"He did not participate in, nor did he authorise, any movement with an aim to avoid that the former congressman make a plea bargain deal or co-operate with justice."
It confirmed that a meeting with a JBS executive had taken place in March but said "there was nothing in the dialogue that would compromise the President's conduct".