Police were called shortly before 9.45am to the David Lloyd leisure centre in Tongue Lane to 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, police said.
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.”
A spokesman for David Lloyd leisure centre said: "We are deeply saddened by today’s incident at our Leeds club. "The child was swimming with his family in our indoor pool at the time of the incident. "He was found unconscious just after 9.30am this morning, and was rescued from the water.
"Our club teams are fully trained to deal with incidents of this nature, and they immediately administered CPR and the emergency services were called. "He was taken to hospital by ambulance, accompanied by his mother. "All of our team at the club are deeply shocked and our thoughts are very much with the boy’s family at this very sad time."Read more at: https://www.yorkshireeveningpost.co.uk/news/tributes-paid-to-three-year-old-boy-who-drowned-in-leeds-pool-as-police-investigation-continues-1-9128464
A West Yorkshire Police spokesperson earlier said: "A three-year-old boy has been taken by ambulance to Leeds General Infirmary with drowning-related injuries.
"The pool has been closed at this time."
Police were called to the club after a report that a child had entered the pool and drowned.