Although AC Milan have been suggested as a potential destination in the past, Sky Sports News says that Aurier may instead make the switch to Russia.
The report suggests that the right-back is happy to move to Spartak, where he feels that he will be provided with more first-team opportunities.
Despite making 42 appearances in all competitions during the last campaign, the 27-year-old has not played a single minute in Spurs' opening three matches.
Aurier has less than two years remaining on his contract at the North London side. body check tags ::