Officers were called shortly before 9.45am to the David Lloyd club on Tongue Lane in Moortown following a report that a child had entered the pool and drowned.
The boy was taken to Leeds General Infirmary where he was later pronounced dead.
Officers said they are treating it as a "tragic accident" but are investigating and appealing for anyone who was in the pool at the time to make contact.
Detective Inspector James Entwistle, of Leeds District CID, said: “This appears to be a tragic accident and are thoughts are with the boy’s family at this extremely difficult time.
“While there is nothing to suggest that the death was suspicious, we do have a duty to investigate the circumstances of what has happened.
“We understand that there were a number of people in the pool at the time who have left the area prior to police arriving at the scene. We would ask these people to come forward to give their accounts of what they have seen and heard.
“Anyone who can assist our enquiries is asked to please call Leeds District CID via 101, quoting log 607 of 21/04.”
Contact can also be made with the police on the live chat system which is found on the contact us section of the West Yorkshire Police website.