U.S. Special Representative for North Korea Stephen Biegun, right, talks with South Korea's Special Representative for Korean Peninsula Peace and Security Affairs Lee Do-hoon during their meeting at the foreign ministry in Seoul on May 10, 2019. Reuters

Stephen Biegun, the diplomat who has been leading efforts to revive stalled U.S. denuclearization talks with North Korea, is under consideration to be President Donald Trump's next ambassador to Russia, a source familiar with the matter said on Monday.

The current ambassador to Moscow, Jon Huntsman, is due to step down in October after two years in the post, the State Department said last week, amid speculation he plans to run for Utah governor.

Vox news on Friday quoted two people familiar with internal White House discussions as saying that Biegun, the current U.S. special representative for North Korea, was Trump's likely choice for Moscow.

A source familiar with the matter told Reuters that Biegun's name was under consideration.