Microsoft declined to comment. TikTok and ByteDance did not immediately respond to Reuters' requests for a comment outside regular business hours.
TikTok, which has about 170 million American users, was briefly taken offline just before a law requiring its Chinese owner ByteDance to either sell it on national security grounds or face a ban took effect on January 19.
Trump, after taking office on January 20, signed an executive order seeking to delay by 75 days the enforcement of the law.
Trump said last week that he was in talks with multiple people over buying TikTok and would likely have a decision on the popular app's future in 30 days.
The US president has previously said he was open to billionaire Elon Musk buying the social media app if the Tesla CEO wanted to do so. Musk, however, has not publicly commented on Trump's offer.
More recently, AI startup Perplexity AI on Sunday made a proposal to merge with TikTok, with the US government getting up to half of the new company in future, a source told Reuters on Sunday.
The reported talks mark the second time that Microsoft has been in the frame to acquire TikTok.
During his first term, Trump ordered TikTok to separate its US version from ByteDance citing national security concerns.
Microsoft emerged as a top bidder in 2020, but the talks soon collapsed, and Trump's divestment push ended a few months later when he left office.
Microsoft CEO Satya Nadella called that deal the "strangest thing I've ever worked on."
The US government had a "particular set of requirements and then it just disappeared," he said in 2021.
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