The Russian club, who are understood to have had an initial enquiry for the Republic of Ireland winger rebuffed by Celtic last week, broke their silence on the speculation for the first time yesterday.
Following repeated denials of interest in McGeady, a Spartak club spokesman changed tack when he said: "So far, Spartak has no comments on his (McGeady) move to give."
It was earlier claimed Spartak, who will play in the Champions League next season, were prepared to offer Celtic around 8 million for McGeady. But it is believed the Parkhead club have placed a valuation in excess of 10 million on the 24-year-old who still has three years of his contract to run.
Hearts owner Vladimir Romanov, meanwhile, responded to the prospect of McGeady playing in his homeland by launching another barbed criticism of both the Old Firm clubs and the general standard of Scottish football.
"If Aiden McGeady moves to Spartak Moscow, he will have to finally start playing football, not just pushing other players like in Scotland," said Romanov. "Also, in Russia there are only 11 players on the pitch, not 12 like in the Glasgow clubs."
A McGeady move to Spartak is being given serious credence in the Russia where Andrei Kanchelskis, the former Rangers and Manchester United winger, offered some advice to the Glasgow-born player.
"A lot will depend on his own resolve to stay in Russia and play," said Kanchelskis. "Patience will be necessary to get used to it all. To master at least the basics of the language really is a must. Without talking to your team-mates, it is going to be hard to play to your full ability.
"In Russia, everything will initially seem different to him. Beginning with food at the training base and ending with relations between the people. The pitches are mostly of worse quality than in Scotland, especially in spring and autumn. The teams play football differently. Naturally, it is not going to be easy."
McGeady is seen as an integral part of the Celtic first team by prospective new manager Neil Lennon who is still waiting to learn if he will be handed the job by the club's board.
A move to recruit Finland coach Stuart Baxter in a mentoring role for Lennon has failed to ignite much enthusiasm among Celtic supporters.
Also, the Finnish FA are opposed to the prospect of Baxter working for Celtic on a part-time basis.
Former Parkhead defender Paul Elliott believes the hot-housing of Rangers manager-in-waiting Ally McCoist under the experienced wing of Walter Smith is the kind of blueprint Celtic should be following with Lennon.
"Neil is a young man and I think experience is always vital," said Elliott. "Ally McCoist has had an excellent mentor in Walter Smith.
I think somebody of that magnitude would be a positive acquisition for the club."
Celtic will face Sporting Lisbon in a pre-season exhibition match at Fenway Park, home of the Boston Red Sox baseball team, on 21 July. The 'Fenway Football Challenge' will be the first football match played at the venue since 9 July, 1968 when Pele lined up for Santos against the Boston Beacons.