The Brazil midfielder, 34, and United management have announced he will leave when his contract expires at the end of June.
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But
Robson told BoyleSports: "I would encourage Casemiro to stay. He's had a really good season this year. He's a top player. He's got a great football brain. He's a really good passer of the ball.
"He heads the ball well and when he goes in to tackle, he means it. You don't stay at Real Madrid for the amount of years he did and win Champions League titles if you're not an absolute top player.
"People see what you're really good at. So I think next season he could definitely give us a little bit more with his experience. He was great in Europe last year too."