The Sunday Express reports that Arsenal boss Arsene Wenger is keen to sign the 27-year-old, as both Manuel Almunia and Lukasz Fabianski have failed to impress this season.
Reina has been a key player at Anfield since joining Liverpool in 2005.
Arsenal have also been linked with Bayer Leverkusen keeper Rene Adler and Lyon’s Hugo Lloris.