According to the Politico media outlet, citing sources close to the attorney general, Sessions’ offer came just before the first foreign trip of Trump's and came in response to the president’s negative reaction to the fact that Sessions decided to recuse himself from the investigation into Russian interference.
Both the White House and the Justice Department declined to comment on the issue.
In May, the Justice Department appointed Muller as special prosecutor for the alleged Russian interference in the US election, a decision which Trump called "the single greatest witch hunt in history."
Russia has repeatedly denied US claims that it meddled in the vote, calling such allegations absurd. Kremlin spokesman Dmitry Peskov has said Moscow did not have official contacts with Trump's team during the presidential campaign.