New York Times columnist Maureen Dowd said on Saturday that Romney is "considering" the offer from the show's producer, Lorne Michaels.
"Well, I think it would be okay," Donald Trump told Fox & Friends on Monday. "He's actually got a great personality and a sense of humor. I think it would be okay -- a little bit different, but I think it wouldn't be bad for him, actually."
Trump said if Romney does host the show, he should use "discretion" to avoid ending up in an awkward situation that Democrats could use in anti-Romney campaign ads.
Former New York Mayor Rudy Giuliani -- in November 1997 -- dressed up as an Italian grandmother as part of an SNL skit. "It haunted Rudy for years to come," Trump said. "So you have to be a little bit careful."
Trump himself has hosted the show, and he says the producers offered him "about 35 different skits, and I could pick the ones I wanted."
This past weekend, SNL opened the show with a bar scene mocking Romney and five other Republicans (Santorum, Perry, Cain, Bachmann and Gingrich) who also ran for the Republican presidential nomination.