Special counsel Robert Mueller is looking into a meeting between longtime Donald Trump adviser Roger Stone and a Russian national during the height of the 2016 presidential campaign, according to Mr. Stone’s friend Michael Caputo, who is a witness in the probe.

Mr. Stone didn’t disclose the meeting, which he says was prompted by an offer of information detrimental to Democratic presidential nominee Hillary Clinton, in his testimony before congressional investigators in September. He is now alerting House Intelligence Committee...