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The pair are set to wed this summer after meeting on "The Bachelorette" several years ago during the show's 12th season in 2016.
However, the duo revealed that the viral outbreak has prompted them to consider delaying their wedding.
Fletcher, 29, and Rodgers, 31, revealed the inside information during an Instagram Live "group date" hosted by Chris Harrison and Lauren Zima.
“We haven't announced the date of our wedding yet, but it is this summer," said Fletcher of the upcoming ceremony, per Entertainment Tonight. "But today our wedding planner actually called me and was like, 'Hey, where's your head at with everything?' And I was like, 'Well, we're good. Like, we're just going to wait until the last minute to see if we need to reschedule.' And she said to us, 'Totally hear you, but the problem with that is that your venue now is starting to book up through up until 2021.'"
Fletcher said they plan to do whatever they can to make their wedding special, even if that means postponing the ceremony.
"We would never sacrifice that day to just rush and get it done. So, if it can't happen the way we want it to happen, we'll do it when we can," she said.
"And I know like, with Jordan, we can't push it to fall," Fletcher added, referencing Rodgers' career as a sports commentator. "So, that's the struggle."
Rodgers joked: "It's been four years, so what’s another year?"
The joke surprised Fletcher, but he assured her he was only "kidding."
However, he noted that postponing until 2021 is a possibility in an effort to keep the wedding "authentic to" the couple.
"We don't want people to be worried about traveling around it, so if there is that, then we'll look at possibly rescheduling to next year even though that’s not what we want to do," Rodgers said.
"The Bachelorette" is among the many shows to have made production adjustments in the wake of the coronavirus outbreak, having canceled production in Italy.
Other popular shows such as "Riverdale," "Stranger Things" and "Survivor" have also halted production to slow the spread of the virus.