Jordan Sullivan was last seen on Valentine's Day in Naburn, near York. He had taken off his clothes and was running towards the River Ouse.
Last week, his mother Nikke Jobling returned to the scene to issue an emotional appeal to her son.
She said: "I don't need to say I love you, and all the family and everybody loves you. But come home. Come home to your family. Jordan. We just want to know you are safe."
North Yorkshire Police says its Community Support Officers have carried out daily checks of the riverside in the three weeks since Jordan went missing.
Inspector Jo Brooksbank has issued a statement urging Jordan or anyone who has seen him to get in touch.
– Inspector Jo Brooksbank, North Yorkshire Police
Despite our ongoing efforts to locate Jordan, sadly he remains missing.
“I urge anyone who may have been in the area on Valentine’s Day to cast their minds back and see if they can recall something that could help with this enquiry.
“I would also like to repeat our plea to Jordan, if you see or hear this appeal, please let your family, friends or the police know you are safe. They are sick with worry and desperate to hear from you.”