However, the Republic of Ireland winger is now entering the last 12 months of his contract and the Russians will take a hit on his transfer value before he walks away for free.
New Goodison boss Roberto Martinez is a long-term admirer of the 27-year-old and tried to buy him for Wigan in January.
However, the proposed £5m switch collapsed at the 11th hour. Now Martinez is ready to move again for the Glasgow-born player. He said: “Over the next few weeks we have to make sure we bring in the right characters as well as the right players.
“It’s not going to be a case of bringing anyone at any time. It’s important we identify the type of help we need in the dressing room and make sure they are the type of footballer who will fit in with the train of thought of this club.
“We need to remember that finishing sixth in the league last season is impressive. It was no accident.”
Martinez, who took over from Davie Moyes after Wigan were relegated, knows he will face stiff competition for McGeady. Paolo di Canio is also in the hunt at Sunderland. The Italian already has McGeady’s Republic of Ireland team-mates John O’Shea, James McClean and Keiren Westwood at the Stadium of Light.