The 25-year-old is set to be available on a free transfer when his contract expires at the end of the season, with the Frenchman’s future in the Italian capital in doubt.
And Diakite’s agent Ulisse Savini has claimed the centre-back’s preferred move would be to the 18-time English champions.
“Liverpool is our first option for June,” Savini told tuttomercatoweb.com.
“It’s in issue in progress and we have to talk yet.
“Everyone knows that the contract is expiring. Also, Lazio know there is no hurry.
“We’ll see in the coming days. However, it would be hard to say no to Liverpool.”
“We got Sturridge in early on and obviously young Coutinho will be a terrific signing for us. He’ll add that excitement and offensive threat at the top end of the field,” said Rodgers.
“I can’t see any more coming in.”