29-year-old Moses spent last season on loan at Inter, but the Nerazzurri turned down the chance to re-sign him.
And according to Russian sources including Sports.ru, the Nigerian will soon be a Spartak player.
The loan deal will include an option for Spartak to buy Moses for €10m, it is reported.
Spartak boss Domenico Tedesco has been desperate to add a right wing-back and Moses can play that role.
The Russian transfer window remains open, allowing Spartak to bring in Moses from Chelsea.
Chelsea signed Moses from Wigan in 2012 and despite playing a part in the Blues’ 2016-17 league title win, he has often been loaned out.
Moses has had temporary spells at Liverpool, Stoke, West Ham, Fenerbahce and Inter.
Lagos-born Moses won 38 caps for Nigeria between 2012 and 2018, scoring an impressive 12 goals.
However, he called time early on his international career, officially retiring from the Super Eagles in August 2018.
Spartak have now made Moses’ loan move from Chelsea official.
🇳🇬 Victor Moses is a Spartak player!
Spartak Moscow and Chelsea have agreed the transfer of Nigerian star Victor Moses to our club. The loan agreement with the 29-year-old midfielder is until the end of the season with the option to buy!
— FC Spartak Moscow (@fcsm_eng) October 15, 2020