Reina was on loan to Napoli for the 2013-14 campaign and turned in some impressive performances, helping the Partenopei to a third-placed finish and the Italian Cup.
Coach Rafa Benitez has been attempting to keep Reina, who appears to have limited opportunities at Liverpool, but the Spaniard's wage bill is a problem.
However, the latest reports suggest that Reina is willing to take a pay cut to return to Napoli where he would be assured of first-team football.
The Brazilian defensive midfielder could be the man Napoli need having failed to bring in Lyon's Maxime Gonalons and Barcelona man Javier Mascherano.
Lucas' stock at Liverpool has fallen and it is widely believed that he would need to impress in pre-season to have a chance to starting the new campaign in the starting line-up.
Il Mattino believes that Napoli are pressing Liverpool on Lucas' availability and Benitez thinks he is the man for the job.
An added bonus for Napoli lies in the fact that Lucas has an Italian passport, which would mean the 27-year-old wouldn't count as one of their non-EU players.
Napoli are hoping to split Reina's wage bill with Liverpool, but it remains unclear whether they would want a similar arrangement should they take Lucas on loan.