The Italian side are reportedly keen on the Serbian winger.
Chelsea's Filipe Luis in action with Liverpool's Lazar Markovic
The winger is expected to leave Liverpool this summer, with the Mirror reporting that Jurgen Klopp has told him he is free to find another club.
It has been a disappointing two years at Anfield for the Serbian, with last season seeing him shipped out on loan to Turkish side Fenerbache.
Picture Supplied by Action Images - Lazar Markovic
They are now keen to see him leave on a permanent basis according to Sapo Desporto, with several clubs across Europe being linked with potential moves as a result.
And it appears that Lazio have joined that list if the latest report from Il Tempo is to be believed.
They report that the Italian side are in the market for a winger this summer as current star Keita Balde is angling for a move to a bigger club.
Livepool's Lazar Markovic in action with Southampton's Nathaniel Clyne
They view Markovic as the ideal replacement for the 21-year-old and are now expected to make a formal bid to Liverpool in the coming days.
According to the newspaper, they will propose a loan deal at first in an attempt to push through the deal quickly, although that seems unlikely to happen given the previous reports about the Reds desire for a sale.
Liverpool manager Juergen Klopp after the match