The Italian side have proposed a loan deal with a permanent option to buy.
Chelsea's Filipe Luis in action with Liverpool's Lazar Markovic
The Serbian winger is expected to leave Anfield this summer after a disappointing two seasons at the club.
He struggled after joining under Brendan Rodgers in 2014 and spent last season on loan at Fenerbache, where he also failed to shine.
Picture Supplied by Action Images - Lazar Markovic
The Reds are keen to see him leave as a result, with him reportedly among several squad players that Jurgen Klopp has told to find a new club.
One option may be Serie A side Fiorentina, who Gazzetta dello Sport report have made a move for his services.
According to the newspaper, they have approached Liverpool about taking Markovic on loan for the season with an obligation to make it permanent next summer for €10 million, around £8.3 million.
Liverpool manager Juergen Klopp
It is unknown whether that is an acceptable offer for Liverpool, but previous reports suggest that it would be rejected.
Sapo Desporto reported earlier this week that the Reds would not sanction another loan move, which had ruled Sporting Lisbon out of the running for his signature.
Should that be the case, then it is likely that this latest bid will be rejected, although the purchase option next season makes it worth considering for them.
Liverpool's Jordan Henderson celebrates with Lazar Markovic after scoring the first goal for his side