Such a move would see the Brazilian reunited with former Liverpool manager Rafa Benitez, who guided his side to third place and a Coppa Italia win.
The Reds are reportedly open to offers for the 27-year-old given the intense competition for places in the middle of the park this season for the Reds, after the signing of Emre Can from Bayer Leverkusen.
Lucas's best position in a Liverpool shirt tends to be in a deeper holding position, but following a knee injury he sustained midway through last season, combined with Brendan Rodgers wanting to get the best out of Steven Gerrard's passing range, Lucas lost his place in the side as Gerrard took up the deeper role.
The 27-year-old came was used in a more advanced role which he didn't look particularly comfortable in - notably when Jordan Henderson was serving a three-game ban towards the end of last season.
Benitez was the manager who signed Lucas in 2007 from Gremio for a fee of around £5 million and was used as a rotation option in his first couple of seasons at Anfield.
There were some suggestions earlier on in the window that Napoli didn't believe Liverpool would be prepared to do a short-term deal for Lucas.
It wouldn't be the first time Rafa Benitez will have loaned one of his old signings from Liverpool, following the loan deal for goalkeeper Pepe Reina last season - whose future seemingly remains uncertain.
So far Lucas has played a part in a defensive midfield role during the pre-season, the role which he is more comfortable with. However, though Steven Gerrard has been playing the deeper role, including against Olympiacos, Liverpool may want to keep hold of Lucas if they decide to rotate Gerrard in order to get the best out of their captain.