The report in Veja magazine on Friday quoted an unnamed aide to Temer saying that the Brazilian Intelligence Agency, known as Abin, had been tasked with finding compromising material on Supreme Court Justice Edson Fachin.
Police filmed the aide, Rodrigo Rocha Loures, in March running from a Sao Paulo pizza restaurant parking lot to a taxi with a black suitcase containing 500,000 reais, about $152,500.
Police said they were serving warrants linked to unrelated criminal investigations when they came under gunfire at the Santa Lucia farming estate, some 860 kilometers (530 miles) from Belem, capital of Para state.
Street protests called by leftist groups around the country also appeared to have had only a modest impact, further easing the sense of intense crisis for the center-right president.
A source close to the matter confirmed that the investigation was under way, without giving further details.
Temer needs to maintain sufficient backing in Congress to ward off calls for his impeachment barely a year after he took over in the wake of his predecessor Dilma Rousseff's own impeachment.
Temer's office issued a statement saying: "President Michel Temer never solicited payments to obtain the silence of former deputy Eduardo Cunha."
Lula, 71, is accused of receiving a seaside apartment as a bribe in a much wider corruption scheme investigated by the so-called "Car Wash" probe upending Brazilian politics.
Lula's upcoming court appearance centers around a luxury apartment that he allegedly received from construction company OAS in exchange for illegal favors.
From 2015, indigenous groups have been occupying land they claim, sparking confrontations with ranchers and farmers.
Brazilian authorities need to show "zero tolerance" in letting aggressors get away with such violence against native peoples, the UN office in the South American country said in a statement.
No arrests were announced in the slayings which took place Thursday in a hard-to-access settlement in Mato Grosso state. A human rights group said the killings were part of a pattern of brutal pressure from rich landowners to displace small-scale farmers from lucrative territories.
Brazilian media reported that as many as 20 buses had been set on fire in the last 24 hours.
Temer is staking his legacy on passage of the reforms, which center on changing the costly pension system to increase the retirement age to 65 for men and 62 for women from today's 60 for men and 55 for women.
Public outrage is mounting over allegations, forcing Temer into almost daily denials that he was involved in corruption
Brazilians will be voting next year for two thirds of the Senate and the whole lower house.
US District Judge Raymond Dearie in Brooklyn ordered Odebrecht to pay a total of $2.6 billion, with $93 million going to the United States, $116 million to Switzerland and the remainder to authorities in Brazil.
Here's what we know so far:
The Brazilian Foreign Ministry sent a letter to its embassies late last year instructing their diplomats them to promote events and seminars with an eye on increasing the exports light arms
Brazil recognized the Palestinian state in 2010 and recalled its ambassador from Israel in 2014 in protest at "disproportionate" force used by the Jewish state in the Gaza Strip.
The court, known as the TSE, could in theory scrap the results of the election, forcing either a snap election or for Congress to pick a new interim leader in Latin America's biggest country.