McGeady, 21, has shone for Celtic in domestic and European games this season.
He has been linked with clubs including Newcastle, whose manager Kevin Keegan admits there are "four or five" Scottish-based players who interest him.
But Strachan, reacting to reports that the Republic of Ireland international could move on for £12million at the end of the season, said: "I don't need £12million and I'd rather keep all the good players instead.
"You have to ask when you are selling players like that if you can get replacements."
Strachan added: "We want to keep the good players here and we want to keep them happy."