The 29-year old saw a return to Inter Milan fall through on deadline day after completing a loan spell under manager Antonio Conte. Subsequently, Spartak have opened discussions with an option to make the deal permanent for £8m.
With another week left in the Russian transfer window, Spartak are hoping to secure Moses as a right wing-back for their side, after previously asking about Serge Aurier at Tottenham and Watford's Kiko Femenia, says the Daily Mail.
As it stands, Moses is out of contract next summer and a deal with Spartak will see him complete his sixth spell away from Chelsea after joining the club in 2012.
Moses is not apart of Frank Lampard's plans going forwards and the Blues manager is keen to broker a deal to balance the books after the club's summer spending spree.