Tucker Carlson, the former Fox News host who now has a show on the social network X, has been spotted in Moscow in recent days, leading to speculation in Russia and the United States that he is about to achieve his long-stated goal of interviewing President Vladimir V. Putin.

If so, Mr. Carlson would be the first American media figure to land a formal interview with the Russian leader since he invaded Ukraine nearly two years ago.

Mr. Putin’s spokesman, Dmitri Peskov, has indicated that Mr. Putin was denying requests from Western new outlets because their countries had been “stupefied” by anti-Russian propaganda. But Mr. Carlson has been a defender of Mr. Putin while attackinghis Western critics, placing him at the vanguard of a pro-Putin wing of the American conservative movement.

In a call with reporters on Monday, Mr. Peskov said: “Many foreign journalists come to the Russian Federation every day. Many continue to work here, and we welcome this.” He added, “As for possible interviews with the president, including with foreign media, we have nothing to report at the moment.”

Russian media on Monday showed a black Mercedes van said to be transporting Mr. Carlson around Moscow entering and then leaving the state administrative building that houses Mr. Peskov’s office.

On television and online, Russian state media has treated Mr. Carlson like a visiting celebrity, offering a stream of photos and videos of his various stops — at the airport, dining at a restaurant, taking in the Spartacus ballet at the Bolshoi Theater.