Although formal identification has not been completed, the body is believed to be that of 35-year-old Jonathan Stringer, who went missing from Harehills yesterday. His family have been informed.
The cause of death is not thought to be suspicious.
West Yorkshire Police said:-
"Police believe a body found in a park in Leeds this morning is that of a man reported missing yesterday.
"At 9.40am today, police were contacted by a member of the public who had found the body of a man in woods at Roundhay Park.
"While formal identification is yet to be completed officers have informed the family of Jonathan Stringer, aged 35, from Harehills, who was reported missing yesterday.
"There are no suspicious circumstances and the Coroner’s Office has been informed."
In August, an elderly man died in the park after falling into Waterloo Lake. The 78-year-old had been suffering from dementia and had gone missing from the Lakeside Cafe while visiting with a family member.