The 22-year-old Vega, a business student and model from the northern city of Barranquilla, was named Miss Universe in late January and has said in interviews that she would be willing to travel to the talks.
"We have read with interest your desire to contribute with your good works to reaching peace," the Revolutionary Armed Forces of Colombia, or FARC, said in a statement on their website late on Friday.
"We salute your willingness to travel to Havana, at this time we invite you to make a visit," added the FARC, which has been holding negotiations with the government in Cuba since late 2012.
The FARC did not say how Vega's visit would help advance the peace talks. She has yet to respond to the invitation.
Representatives at the talks have so far reached agreement on three of five agenda points, including land reform, an end to the illegal drugs trade and political participation for ex-guerrillas.
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