Former Culture Minister Marcelo Calero said Mr Temer asked him to help another minister in a personal business deal.
He said he was asked to allow construction of luxury apartments in a historic district of Salvador.
Mr Calero, who resigned last week, had previously blocked the plans. President Temer has denied the allegations.
However, he admitted talking to Mr Calero about the project.
The president has vowed to clean up corruption in Brazil, but has lost three ministers to corruption allegations.
The scandal involves government secretary Geddel Vieira Lima, who had bought a property in Salvador in Bahia state.
Analysis: Daniel Gallas, South America Business Correspondent
Barely six months after coming to power, and still with his legitimacy being questioned by many, this is the second major corruption scandal to rock Michel Temer's government.
This time the president himself is implicated in allegations.
Marcelo Calero, who is making these allegations, is a career diplomat and an outsider to mainstream politics.
The government said Mr Calero misunderstood some of the conversations and that no pressure was meant in any of them.
But critics ask: why would the Brazilian president bring up a personal business deal of one of his key allies in the first place?
Brazil's opposition - still bitter about the demise of President Dilma Rousseff in an impeachment process fuelled by Mr Temer's allies - is already calling for the new president to be removed from power.
Mr Calero's ministry vetoed the construction, on the grounds that the proposed building was on a heritage site.
He told the police both the president and the minister had pressured him to overturn the decision.
Earlier this week, an ethics panel decided to open an investigation into Mr Lima over the allegations, before the president's alleged involvement came to light.
Despite pressures to sack Mr Lima, Mr Temer said the minister will keep his job.
Mr Temer came to power earlier this year, after former President Dilma Rousseff was impeached during a lengthy political crisis that gripped the country.
She was accused of manipulating the budget, but maintained her innocence and said that her political opponents has carried out a "parliamentary coup".
Mr Temer has since tried to maintain a stable government, but has been plagued with corruption allegations against his own party.