According to The Metro, Rodgers had a bid rejected last summer but he's ready to go back in for the 19-year-old forward and match Lazio's £15m asking price.
Luis Suarez update
Liverpool will reportedly offer the full £15m in January to sign the striker, with Balde Diao keen to move to Anfield ahead of Arsenal.
The Gunners scouts have been watching him closely in Italy, but the teenager believes he stands a better chance of immediate first-team football in Liverpool.
His agent, Ulisse Savini, did not deny that his player could leave Italy saying 'it's too early to say what will happen.'
Spanish-born Diao was with the Barcelona academy until 2011, when he moved to Italy to play for Lazio. Since breaking through into the first-team last year, he has made 23 league appearances, scoring five goals.
Premier League interest
Arsenal and Liverpool were both in the market for a striker over the summer, and Diao was on both Premier League clubs' radar. Ultimately, Arsene Wenger signed Danny Welbeck on deadline day from Manchester United while Rodgers brought former-City forward Mario Balotelli to Anfield.
The Italian international looks like he may take time to settle into life at Liverpool, and Rodgers will continue his search for striker options at the earliest opportunity in January.
Diao could be the man they turn to although it remains to be seen whether Arsenal rekindle interest.