In a statement published on their website, the group said they were taking up an offer made by Colombia's Paulina Vega in her quest to win her title.
Ms Vega, 22, has so far not responded to the offer.
The rebel army has been in talks with the government for the past two years.
It has waged an anti-government guerrilla war for the past 50 years.
Representatives of both sides are trying to strike a deal but the talks in the Cuban capital, Havana, are deadlocked.
Agreement has so far been reached on issues of land reform and bringing the Farc into formal politics, but a final peace deal remains elusive.
During interviews prior to being crowned Miss Universe, Ms Vega had spoken of wanting to see peace in Colombia.
In their statement, Farc rebels said they welcomed her "willingness" to travel to Havana, adding: "We invite you to materialise your visit to update you about the development of the peace talks."
The BBC's correspondent in Havana, Will Grant, said it was surprising that the group would act on Ms Vega's sentiments.
Some 220,000 people, most of them civilians, are estimated to have been killed since the Marxist-inspired Farc rebels launched their armed struggle in 1964.
Rebels from Colombia's Farc militia have invited the newly crowned Miss Universe to assist their peace negotiations with the government.