The Republic of Ireland international is free to talk with other clubs this month, as his deal with the Russian club is set to expire in the summer.
McGeady has no intention of signing a new deal at Spartak, after falling out with manager Valeri Karpin.
The 27-year-old has long been linked with a move to the Premier League, after previously admitting that watching English football left him feeling ‘jealous.’
Everton are understood to be close to reaching an agreement with the winger over wages.
Once that is sorted, Martinez may attempt to agree a cut price fee with Spartak to bring McGeady to the Premier League this month, which may be easier than expected considering he remains out of favour.
Tottenham managed a similar deal with Lewis Holtby last season, and Martinez would be keen to add reinforcements for the second half of the season, with Everton currently just a point outside the Champions League places.
The former Celtic man joined the Russian side for £9.5million in 2010, and has made 72 league appearances, scoring 11 goals.