It's the first such commitment by Trump, who has dismissed the ongoing investigations into whether his campaign colluded with Russia as a "witch hunt" invented by Democrats to explain Hillary Clinton's loss.
It wasn't immediately clear exactly how the payouts would be structured or which aides would be receiving them. The official spoke on condition of anonymity in order to discuss the president's plans, which were first reported by the website Axios.
Mueller's team of investigators has been interviewing current and former White House officials in their probe, and Trump campaign officials and others have been turning over tens of thousands of emails and documents to federal and congressional investigators.
One former campaign aide, Michael Caputo, has spoken publicly about the financial toll the legal bills have taken on his family, including having to empty out his children's college savings accounts.
Trump has repeatedly denied that he colluded with Russia to win the election and has voiced skepticism about the conclusion by US intelligence agencies that Russia had a clear preference for Trump in the 2016 campaign.
The continuing investigations and attention to the issue have infuriated the president, who sees the efforts as an attempt to delegitimise his presidency.
Facebook has said ads that ran on the company's social media platform and have been linked to a Russian internet agency were seen by an estimated 10 million people before and after the 2016 election.
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