Trump gave the order in June 2017, according to the Times, but White House counsel Don McGahn refused, saying it would have a "catastrophic effect" on Trump's presidency.
In the Oval Office on Tuesday, Trump said he was "not at all concerned" about what Sessions may have told the Mueller team.
The intelligence community believes that the Russian government was engaged in electoral interference during the 2016 US presidential election.
US intelligence chiefs have told congress Russia meddled in the election, but Putin has repeatedly denied any Russian involvement.
Trump said Saturday he believes Vladimir Putin is being sincere when he denies meddling in the US election that propelled Trump to power.
A Russian lawyer has said Donald Trump Jr suggested in a meeting during the US presidential campaign that a law imposing sanctions on Russia could be reviewed if his father were elected.