A senior White House official confirmed aides have been urging Trump to keep Sessions but said it was because "he's the best man for the job."
A spokeswoman at the Justice Department declined to comment.
Trump has repeatedly shrugged off advice from close aides.
Earlier this week, he said the Justice Department led by Sessions was wrong to submit a "watered down, politically correct" version of his proposed travel ban on people from several Muslim-majority countries to the Supreme Court."
The outburst weakened government lawyers' defence that the travel ban, which has been blocked by federal courts, was not intended as a ban on Muslims.
Sessions offered to resign because of tensions with Trump over his decision to recuse himself from a federal investigation into ties between Trump's associates and Russian officials when Russia was allegedly meddling in the 2016 US presidential election, according to media reports.
A former senator, Sessions was one of the first senior Republican lawmakers to endorse Trump as a presidential candidate and played an important role in the campaign.
He recused himself from the Russia investigation in March after he failed to disclose a meeting he had with Russia's ambassador in Washington.
Trump and Sessions were together at the White House on May 17, when Deputy Attorney General Rod Rosenstein surprised them both by appointing former FBI Director Robert Mueller as special counsel to head the Russia investigation.