Rose revealed the meeting Tuesday morning during the CBS news panel at the Television Critics Assn. press tour in Pasadena.
"A friend of mine named Sean Penn has been in the news," Rose told the room of reporters. "So I went to see him last night" for upcoming CBS piece.
Penn has been in the news since his interview with Guzman, one of the most wanted men in the world, was published on the Rolling Stone website Saturday. The article revealed that the actor traveled to Mexico to interview the drug lord in October, while Guzman was on the run from Mexican authorities after escaping prison. The billionaire fugitive was recaptured last week.
Questions have been swirling about whether the actor could face potential legal liability for meeting with the fugitive drug kingpin.
"We're planning to do an interview about his experience," Rose said. "I have a thousand questions for Sean."
"When it will happen," Rose added, "will depend on when we can agree on the date to do it. I would hope sooner than later. I'm prepared to do it whenever I get the green light from [Penn] and his lawyers."
The co-host of "CBS This Morning" noted that he has known Penn for a long time and has interviewed him numerous times on his
"I hadn't seen him, and I was interested in what happened," Rose said. "So I went to talk about that... I don't think he will be doing any other interviews until we sit down."
When asked for his thoughts as a journalist about the ethics in meeting with El Chapo.
"I can't really talk about it right now because we're going to do that for the interview," Rose said. "Clearly, I would have liked to have the opportunity to interview a whole range of people -- El Chapo would have been one of them. All the questions I'm saving for [Sean for] the time we sit down together. There's not much I can say about it now other than it is a remarkable story."