Bellingham, as he was leaving Birmingham City, and his family met with Robson, Sir Alex Ferguson and Eric Cantona at Carrington training ground to discuss a potential deal before signing for Borussia Dortmund.
Robson told The Sun: "I watched him closely playing against (Manchester) City (last week).
"You could see how much he's progressed since we thought we had landed him at Manchester United a couple of years ago."
Robson went on to add: "Unfortunately for us he decided to move to Germany. We thought we more or less had him.
"Myself, Sir Alex and Eric Cantona all met him with his mum and dad at Carrington and after that meeting we thought he was coming to us."