Vilnius mayor Remigios Simasios said on Monday he was offering the players to come to one of the city's finest restaurants and there would be a table reserved for them.
The call followed Ronaldo's comments as he sided next to Messi at the European Footballer of the Year awards in Monaco on 29 October.
Ronaldo said that despite the fiercely contested Messi for many years, "we have never had dinner together before."
"Ronaldo's initiative to sit next to Messi for dinner resonated with the gourmet dining in Vilnius," Simacius said.