The People says Anfield spies have been to check on the 21-year-old and the Kop chief sees him as the eventual replacement for Robbie Keane.
The Anfield club have been a striker short since Keane returned to Spurs and Benitez wants someone in for next season.
Diogo has been at Olympiakos since August and hopes to qualify for an EU passport soon. He is uncapped by Brazil at full international level but was in their Olympic squad, only to miss out through injury.
Benitez loaned left-back Sebastian Leto to Olympiakos last August and could even include the Argentine defender in a swap deal.