Emergency services are continuing to search for the 32-year-old man after being called to Horbury Lagoon at 7pm yesterday.
West Yorkshire Police said the man is believed to have drowned as they issued a warning to others about the dangers of swimming in open water.
A force spokesman said they called to a report that the Eastern European man, from the Leeds area, had got into difficulties while swimming in the lagoon.
Police, fire and ambulance services attended the scene but, despite numerous searches, the man has not yet been found.
Searches are expected to continue throughout today.
Superintendent Marianne Huison, of West Yorkshire Police, said: "We are continuing inquiries at the scene of this tragic incident and, while the male has not yet been recovered, it is, at this time, believed he has sadly drowned.
"I would like to remind all residents in, and visitors to, West Yorkshire of the extreme dangers posed by swimming in or entering open water at lagoons or industrial sites.
"Such water can be very cold, even in the summer months, and people suddenly entering cold water are susceptible to hyperventilation, which could result in the body going into seizure.
"There can also be hidden currents and unseen dangers such as mud banks or items under the water which a swimmer can become caught on.
"Our inquiries at the lagoon to locate this male are expected to continue throughout today and potentially into Monday and officers are working to support his family at this time."