talkSPORT reports that the Spanish winger has arrived at the Italian club to have a physical before signing a five-year deal.
23-year-old Alberto joined the Reds from Sevilla in 2013 but has failed to force his way into calculations at Anfield and has spent the past two seasons on loan with Malaga and Deportivo La Coruña.
Alberto will now link up with Simone Inzaghi in Rome.
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