The Gunners had £20m bid for the Spaniard rejected by their Premier League rivals previously, but are tempted to return following his recent troubles at Anfield.
Reina has struggled for form so far this season, making a series of uncharacteristic errors before suffering an injury whilst on international duty.
Back-up stopper Brad Jones has been filling in and appears to have impressed his manager Brendan Rodgers.
This has led to speculation that the Northern Irishman may be tempted to cash in on the 30-year-old to raise funds for strengthening his squad during the winter.
The North London club have long suffered with a lack of a stable number one, with the likes of Manuel Almunia filling the role, but not to a suitable standard.
Polish international Wojciech Szczesny has impressed recently, but Wenger is believed to be unconvinced as to whether the young keeper is the long-term solution for the club.
Reina may be open to a move after previously revealing his disappointment at seeing Arsenal’s last bid rejected:
“Arsenal had made their determination to sign me clear by offering £20m, a phenomenal amount for a goalkeeper. Part of me felt that I was well within my rights to consider my future even if I did so with a heavy heart.”