"We have read with interest your desire to contribute to peace and reconciliation among Colombians. We acknowledge your willingness to travel to Havana and we invite you to materialize your visit to update you about the development of the peace talks," rebels said in a statement published on their website.
FARC declined to elaborate on how Vega's possible visit to Havana could help advance the peace talks.
The 22-year-old Vega, who is a business student and model from the northern Colombian city of Barranquilla, was announced Miss Universe late last month. She has yet to respond to the invitation.
Despite the fact that the sides have already agreed on issues of land reform and bringing FARC into formal politics, a final peace deal remains deadlocked.
More than 200,000 people, mostly civilians, have reportedly been killed since FARC rebels began fighting in Colombia in 1964.
