The 28-year-old Preuvian international is set to leave the Stadio Artemio Franchi this summer after joining the Serie A outfit back in 2008.
Reds boss Kenny Dalglish is considering an attempt to bring him to Anfield at the end of the current campaign, but will face stiff competition for his signature from Bayern Munich and Zenit St Petersburg.
Liverpool are likely to be active in the transfer market again after a disappointing Premier League campaign, with the Merseyside club likely to miss out on Champions League football once again next season.
After winning the Carling Cup last month, Dalglish's side have already guaranteed their place in the Europa League, but the Liverpool boss will be hoping that bringing in players of Vargas' calibre will help take the club to the next level.
Fiorentina are open to the prospect of selling the attacking midfielder but will be looking to start the bidding at around £15million, and hope that the high interest in the sought-after South American will allow them to reach their transfer target.
Vargas could be swayed by the opportunity of a fresh challenge in a new country, and Liverpool will be hoping they can match his ambition. However, with potentially lucrative offers in Russia and Germany on the table, they may have an uphill battle.