Provided are a computer program product, system, and method for using a machine learning module to determine an allocation of stage and destage tasks. Storage performance information related to processing of Input/Output (I/O) requests with respect to the storage unit is provided to a machine learning module. The machine learning module receives a computed number of stage tasks and a computed number of destage tasks. A current number of stage tasks allocated to stage tracks from the storage unit to the cache is adjusted based on the computed number of stage tasks. A current number of destage tasks allocated to destage tracks from the cache to the storage unit is adjusted based on the computed number of destage tasks.