Citing reports in Russian newspaper Izvestia, it is claimed that Rubin are ready to make a £9m offer for the Senegalese frontman.
Arsenal and Spurs have been heavily linked with Sow in the past, and the report suggests both tried and failed to sign him last season.
Sow currently plays his football in Turkey for Fenerbahce, but he could be on his way this summer with several clubs keen.
The former-Lille striker was reportedly a target for Arsenal and Tottenham last summer, when both clubs were looking to add to their options up front.
Spurs eventually signed Roberto Soldado, while Emmanuel Adebayor has been brought in from the cold under new boss Tim Sherwood.
Arsenal meanwhile added only Yaya Sanogo before the beginning of the campaign.
And while they were expected to strengthen in the January transfer window, Gunners boss Arsene Wenger failed to sign a striker, instead bringing in Kim Kallstrom on loan from Spartak Moscow.