Speaking at the opening day of the Grassroots Football show at the NEC, Robson said: "I know how much Sir Alex likes him as a player and the fans adore him. So I don't see where Ronaldo gets anything out of leaving Manchester United for Real Madrid.
"You just look at the Champions League this year, Man Utd have won it. They are the richest club in the world. He's got 75,000 fans who absolutely adore him.
"You think that the grass is always greener. But I think it would be a big mistake for him to leave at this moment in time.
"I had it myself in 1983. I had a good run in the Cup Winners' Cup and AC Milan, Juventus and Sampdoria were after me. As soon as I knew that Manchester United wanted me, I was happy to sign a new contract.
"You never know how the agents are operating. You don't know until you speak to him what his thoughts are. If it's only his agent going out there saying there's an interest, then you need to know what's happening.
"According to his agent, money is coming into it. If Manchester United offer the same money, then he's happy to stay.
"But sometimes as a player you have to make your own mind up and not bother listening to your agent. If you are loving your football and you have just won the Premier League and Champions League double, I'd be happy to stay where I was.
"It wouldn't matter to me if they had offered £30,000-a-week more because of the money some of these lads are on now, it's less of an issue than playing in a successful side."