Players on the 40-man roster can be moved up to the major leagues after Sept. 1.
At least one move that is expected to happen in the coming days is to add right-hander Erik Johnson to the big league roster. Another candidate to be called up is infielder Marcus Semien.
This is Leesman’s second stint with the White Sox this season. He gave up one run on four hits over five innings in a no decision in his major league debut Aug. 9 against the Minnesota Twins and was sent back down immediately after the game.
Anderson, who will give the White Sox catching depth over the final month, has 25 games of major league experience, all with the St. Louis Cardinals. He was signed as a free agent this past offseason.
The White Sox’s 40-man roster is now at 37. Johnson and Semien would need to be added to the 40-man roster before they could be called up.