The 19-year-old from Ladbroke Grove in west London disappeared two weeks ago after telling his mother he was going out to visit a friend.
He was last seen in CCTV footage walking along Smarts Lane towards the forest at 12.39am on 23 March after taking a taxi to Loughton in Essex.
Officers with dogs have been searching the area for the past four days and police divers were seen searching ponds on Sunday.
On Monday afternoon the Metropolitan Police, which has been leading the investigation, said they had been informed by Essex Police that a body of a male had been found.
The body has yet to be formally identified but Mr Okorogheye‘s mother, Evidence Joel, said police had informed her “the description matches his”.
She told the MyLondon website: “Oh God, they said the description matches his, but we’ll go in tomorrow to find out.”
The Met Police said in a statement: “Enquiries are underway to identify the body.
“Detectives investigating the disappearance of 19-year-old Richard Okorogheye are aware.
“Richard’s family are being supported by specially trained officers and kept updated with developments. Officers remain at the scene and enquiries continue.”
Mr Okorogheye, a student of Oxford Brookes University, went missing after shielding since the start of the pandemic because of his medical condition, sickle cell disease.
Shortly before his disappearance he had told his mother he was “struggling to cope” with the pressure of studying online.
He left his home at approximately 8.30pm and boarded the 23 southbound bus in Ladbroke Grove at 8.44pm on 22 March. His family reported him missing on 24 March.
Ms Joel said her son had told her he was going to visit a friend’s house and would be back later – but he never returned home. None of his friends said they had seen him that night.
Last week she suggested that the Metropolitan police should be doing more to trace the 19-year-old, telling MyLondon: “Richard is seen as a low risk but he’s a young adult with a health condition.”
The UK charity Missing People has previously said black people and those from other ethnic minority groups “are not always getting the response they deserve when they are missing or report someone missing”.