The former Red Devils captain has criticized the Blues for their latest attempt to sign the England striker and believes he can still be part of the club's future plans.
The Blues, who have already seen two bids for the striker rejected this summer, are keen to continue their pursuit of their No. 1 transfer target, with manager Jose Mourinho admitting they will chase him until the final day of the transfer window.
However, Robson - a current club ambassador with the Red Devils since 2008 - believes the most recent offer from the London club is an insult to a player he sees as one of the top six strikers in the world.
"The thing that makes me laugh is I've been told it [the latest bid] is 25-30 million pounds. For Wayne Rooney? A 27-year-old who is probably in the top six strikers in the world?" Robson told talkSPORT. "What are United going to have to pay to replace him? I'm amazed at that. I think it is an insult to Wayne Rooney."
Despite the transfer saga surrounding Rooney, Robson believes the England striker can still be part of the team next season.
"I don't know what's in the head of Wayne and his agent - why he wants to leave. I know he had loggerheads with Sir Alex [Ferguson], but David Moyes is the manager now," Robson said. "To me it is so important for him to concentrate on his football this season. I don't know what he sees - the grass is greener on the other side.
"The fans love him, the players love him so I don't see what the unsettlement is. Everyone would like to see Wayne Rooney settle down and be part of the team to try to retain the title."