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.