The Premier League champions head into the new campaign short of midfield options following the retirement of Paul Scholes at the end of last season.
Former United captain Robson believes that Barcelona playmaker Fabregas would provide new boss David Moyes with much-needed quality in central midfield.
"I think Fabregas is a fantastic player and I hope he's playing for Manchester United next season," he told reporters.
Yorke, a member of the United treble-winning side agrees, cited the Spaniard's reunion with striker and former Arsenal team-mate Robin van Persie as potentially invaluable.
"If we can get him [Fabregas] it would be a fantastic scoop," he added.
"The great thing about him is the fact that he had so many experiences in the Premier League. Him and [Robin] van Persie had a great understanding [at Arsenal] so we know he's a top player."
With continued speculation surrounding want-away striker Wayne Rooney, who has been the subject of a bid from Chelsea, Robson believes that the club need to bring in more options if they want to compete with Europe's big spenders next season.
"We've got a few people in mind who we would like to try and sign," said the former United and England captain.
"You've got to try and bring new players in because Bayern Munich, Barcelona and Real Madrid are all top teams and they want to try and keep improving all the time."
However, should Moyes fail in his bid to bring in more new faces before the transfer window shuts, the club ambassador remains optimistic that the United can continue their great tradition of backing existing players to solve their midfield issues.
"I think it's a great opportunity for the likes of Tom Cleverely and Anderson," he added.
"They've got to step up. They've got to take on that they're a United player so they're going to have a better chance to prove that."