He was accused of authorising illicit payments to a jailed former speaker of the lower house of the Brazilian parliament, Eduardo Cunha.
Cunha was sentenced in March to 15 years in prison for corruption, money laundering and tax evasion.
The accusations against Mr Temer were made by O Globo newspaper.
A massive game-changer: analysis by Julia Carneiro, BBC News, Rio de Janeiro
The content of the alleged recordings is so grave that the shockwaves quickly rippled across the country.
