The winger Thompson, a Bosman signing from Morecambe, missed Saturday's 4-0 win over Grimsby Town because of an hip injury he suffered while using weights in training.
May had to be replaced early in the game, which doubled as the Lincolnshire Senior Cup final, with an ankle injury.
But the Iron manager Nigel Adkins believes both will be fit to play against Leeds at Glanford Park on Saturday.
Joe Murphy, Andy Crosby and Joe Wilcox will all be missing because of injury.