The 27-year-old moved to the Russian capital in a reported £9 million deal in August 2010, becoming the most expensive export from the Scottish top flight in the process.
His Spartak contract expires at the end of the current season, and McGeady has previously expressed a desire to move back to British shores.
"Everything is OK with McGeady and he has gone back to Britain with his family (during the Russian League's winter break)," said Spartak's sporting director Roman Askhabadze.
"His contract runs out in the summer, he was offered a contract extension by us, but he has refused that. He did that for family reasons as his wife and children could not adapt to Moscow.
"Over the winter, if we get an offer which suits Spartak, then McGeady will go.
"But if a suitable offer does not come in, he will be with us until the end of his contract."
