The Peru international has been linked with a move away from the Serie A outfit this summer and the Reds are reportedly among the clubs keen to sign him.
The 28-year-old is under contract with the Viola for another season and has also been linked with a move to La Liga side Malaga.
"There is the possibility that he (Vargas) will leave Fiorentina," Vargas's agent Jorge Cyterszpiler said to tuttomercatoweb.com.
"But at this time it's just a rumour and there is nothing official. He didn't have the best best of seasons and he needs to make up for it next season.
"Liverpool is an option, but there is also Malaga that has the fascination of playing in next season's Champions League. Does he have a preference with regards to playing the Premier League or the Primera Liga? Vargas likes both leagues as well as the Serie A."