The Republic of Ireland international has been training with Spartak's youth team and is expected to leave the club in January.
McGeady, who is out of contract at the end of the season, has been transfer-listed by coach Valery Karpin, with Premier League clubs Aston Villa, Everton, Fulham and Newcastle all reportedly interested.
"McGeady has been removed from practice sessions for failing to comply with the demands of the head coach both during the practices and the matches," said Karpin.
"Now everything depends on him, nobody else. He has the chance to return if he is in form and willing to comply with the demands of the team's coaches.
"Everything else is an internal affair of the club."
McGeady is rumoured to have fallen out with Karpin following last month's 1-0 defeat to city rivals CSKA.
Boris Pozdnyakov, one of Spartak's assistant coaches, said that McGeady had lost his motivation and was not practising and playing at full strength in Spartak's recent matches.
"He (McGeady) has repeatedly issued a desire to continue his career in England," Pozdnyakov told Russian newspaper Sport Express.
"The club head coach couldn't tolerate that so took strict measures. I think he was quite right."
McGeady joined Spartak from Celtic in August 2010 and has scored 13 goals in 83 appearances.