"The rumors are untrue," the ministry said.
Earlier on Monday, media reports said that Moscow Region Governor Boris Gromov had resigned and would be appointed Russia's ambassador to Ukraine, but the governor's press service dismissed the reports as speculation.
The Russian embassy in Ukraine has not commented on the press reports.
Chernomyrdin has been in the post since 2001.
A source in Russia's lower house of parliament said the State Duma's international affairs committee could consider the Gromov's candidacy for the ambassadorial post next week.
The source said Gromov's nomination would be submitted to the committee on December 22.