Jost, who has been promoting his new book, A Very Punchable Face: A Memoir, said he and Johansson have "of course" had to figure out what the future looks like for tying the knot because of all the uncertainty in the world -- and in regard to the actual day-to-day capabilities of the court system.
"We don't know what's even legally allowed, right?" Jost said, adding, "This is also not the time to get all your elderly, at-risk relatives together in one big group."
Jost went on to say that, at this point, they really don't know "when that moment will be" that they can actually have a wedding ceremony.
"We don't know if we could do a live show for SNL yet, let alone have a wedding where the audience is elders," Jost shared.
Jost and Johansson got engaged in May 2019 after two years of dating. The pair have stayed largely quiet about their wedding plans in the months since.
Later elaborating on what Saturday Night Live might look like when season 46 kicks off later this year, Jost admitted to Cohen that they still don't know if the show will be back in the studio or if they will have to keep producing remote episodes from home.
"We're waiting on … what the the New York state guidelines are, and what the rates of infection are, at that point," explained Jost, who serves as both a cast member and head writer on the series.
"Of course we'd all love to do it in the studio and have an audience, and do it as close to normal as possible," he added. "But I don't know which stage we'll be in and what's feasible."
Andy Cohen Live airs Mondays and Wednesdays at 10 a.m. ET on his exclusive SiriusXM channel, Radio Andy.