The Scots began their Group A campaign with a goalless draw at home to Serbia on Saturday, where McGregor's groin injury, picked up in the friendly win over Australia last month, resurfaced.
Speaking at Scotland's Mar Hall training base, manager Levein assessed his three injury doubts and confirmed St Mirren keeper Samson had joined up with the squad.
He said: "Charlie Adam has a wee problem, Matt Gilks picked up a problem in training yesterday (Sunday) and Allan McGregor has the same thing but nowhere near as bad as he was. I am hopeful that all three will make it."
Asked if the Besiktas keeper would require an injection to play, Levein said: "I don't think so and I don't think it is something that we would do, that's more for his club to undertake. He is an experienced player and he will know better than anybody if he is fit to play.
"But I spoke to him and Matt this morning (Monday) and they are fairly positive and so is Charlie. Craig Samson joined us, he is in to train and we will see what happens."