Eligibility Requirements

Here is the helpful link from Indeed.com Guide to Earning Aircraft Dispatcher License

PART 121 - OPERATING REQUIREMENTS: DOMESTIC, FLAG, AND SUPPLEMENTAL OPERATIONS 

To eliminate any doubt as to whether or not these requirements have been met, you should check with your local FAA FSDO office. Note: ATP applicants are no longer required to present their qualifications to an FAA Inspector prior to the test for an FAA authorization. A current First-Class Medical Certificate is no longer required to sit for the exam. Only a 3rd Class is required for the check ride in an airplane. A medical is not required if taking the ride in the simulator.

65.53 Eligibility requirements: General.

65.57 Experience or training requirements.

65.55 Knowledge requirements.