Donald Trump will become the first leading candidate to host the show next month, just weeks after Hillary Clinton made a well received appearance.
And Marco Rubio told CNN's Jamie Gangel this week that he'd consider appearing on the show
"I don't think I've been invited," he said. "We'll see if that makes sense. I'm not going to cancel campaign events to do it."
Even if Rubio doesn't appear, the Florida senator said he wonders who will appear as him.
"I just want to make sure it's the right person," he said. "Somebody said (television host) Mario Lopez the other day. Maybe they'll bring him on as a guest or something."
Lopez thanked Rubio Monday on social media for mentioning him and said he's interested in the idea.
"Let's do it! @marcorubio," the "Extra" host tweeted.
"Rubio! Thank you for the shout out on CNN. I'd be flattered to play you on SNL. I know you only had a couple of Latino options. It was either me or George Lopez and I think you made the right choice. Gracias," Lopez added on Instagram
But SNL fan Ted Cruz was not bashful about his interest in appearing on the show.
"I grew up as a Saturday Night Live junkie, so I love watching," he said Friday on Bloomberg's "With All Due Respect." "I'd be thrilled to do it. I would love to."
When discussing sketch ideas, Cruz shared that he's a huge Eddie Murphy fan.
"The problem is I can actually do quite a few of those riffs, but none of them are appropriate in the world of politics," he said.
Cruz said he's looking forward to watching Trump host, saying the former reality star has a "gift."
"I'm sure Donald will do a terrific job. He has an extraordinary gift and he's a marvelous entertainer."
But Republican front-runner Ben Carson said he has no interest in guest hosting SNL, saying the presidency is "a very serious thing."
"I think the presidency of the United States is a very serious thing and I don't even want to begin to put it in the light of comedy," he said, also on Bloomberg's "With All Due Respect."
"Even though I know the comedians will continue to make fun of me. That's what they do. And that's fine. But they they can do that on their own. I will not cooperate," he added.
But Cruz said he disagrees and that some candidates need to learn how to laugh at themselves.
"I think you should have fun. You should laugh and enjoy yourself. That doesn't stop you from standing up and leading on serious issues," he said. "But too many Republicans have taken themselves way too seriously."