Mr Parry, aged 41, was last seen in the Sundorne area of Shrewsbury on Saturday.
The body was found at Haughmond Hill, near Shrewsbury, by search and rescue teams last night.
Formal identification has not yet taken place but Mr Parry's family have been informed of the discovery.
Holly Claydon-Bevan, spokeswoman for West Mercia Police said: "A body has sadly been found as part of a search for missing Shrewsbury man Lee Parry.
"Formal identification is yet to take place but the family of Lee have been informed.
"The body was discovered at approximately 8.30pm on last night at Haughmond Hill, Uffington, by specialist search and rescue teams.
"The death is not currently being treated as suspicious and the coroner has been informed.
"We would like to thank the public for their help in sharing an earlier appeal."