The 30-year-old's position as first-choice at Liverpool is under serious threat for the first time this season since he joined the club in 2005 following the summer arrival of Simon Mignolet from Sunderland.
He has been heavily linked with a return to old club Barcelona but no bid has been forthcoming so far from Spain.
As a result, he is set to team up with the Reds on their summer tour in Australia next week after being given extra time off having played in the Confederations Cup for Spain in June.
New-boy Mignolet insists he has no intention of sitting on the bench in the new campaign, while boss Brendan Rodgers says the pair will battle it out to be first choice but Reina's future remains in doubt with Benitez keen to sign him again for his new club.
Napoli were hoping to land QPR's Julio Cesar but that deal has apparently stalled and the former Reds boss has now targeted Reina instead, with an offer in excess of £7million set to tempt the Anfield club.
Liverpool last week