A copy of Iran's Farhikhtegan daily newspaper is pictured on a shelf in a kiosk in Tehran with a cartoon drawing of Elon Musk on its front-page. AFP
In an interview with state news agency IRNA, spokesman Esmaeil Baghaei was reported as "categorically denying such a meeting" and expressing "surprise at the coverage of the American media in this regard".
The Times claimed on Friday that Musk, who is a close ally of US President-elect Donald Trump, met earlier this week with Iran's ambassador to the UN, Amir Saeid Iravani.
It cited anonymous Iranian sources describing the encounter as "positive".
In the weeks leading up to Trump's re-election, Iranian officials have signalled a willingness to resolve issues with the West.
Iran and the United Stated cut diplomatic ties shortly after the 1979 Islamic revolution that toppled the US-backed shah of Iran, Mohammed Reza Pahlavi.
Since then, both countries have communicated through the Swiss embassy in Tehran and the Sultanate of Oman.
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