Variable sleeve clearance control systems for gas turbine engines are disclosed. An example variable sleeve clearance control system for a gas turbine engine includes a sleeve comprising a first end and a second end, the first end of the sleeve coupled to a first spring that biases the sleeve inward, and the second end of the sleeve coupled to a second spring that biases the sleeve outward, a proximity sensor to measure a clearance width, and a controller for each of the first and second springs, the controller to obtain the measured clearance width from the proximity sensor and determine a response of the first and second springs.