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, with Michael Carrick United's most experienced central midfield option alongside veteran winger-cum-midfielder Ryan Giggs.
With Scholes' influence in particular set to be missed, Robson believes that Barcelona playmaker Fabregas would provide new boss David Moyes with much-needed options.
"I think Fabregas is a fantastic player and I hope he's playing for Manchester United next season," said Robson.
Yorke, a member of the1999 United treble-winning side agrees, citing 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," said Yorke.
"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, Robson went on to say that he expects England international Rooney to remain at Old Trafford.
"David Moyes has said Wayne Rooney isn't for sale and as far as we're concerned that's the end of it," he added.
But Yorke admitted he can see the attraction of wanting to play for new Chelsea manager Jose Mourinho, although he is unsure on whether the Portuguese can replicate the success of his first spell at the club, which brought two Premier League titles in three years between 2004 and 2007.
"The special one. He's special isn't he, and he's got that 'wow' factor obviously," Yorke said.
"Can he come back and do the same with a different bunch of players? I think it's certainly an exciting time at Chelsea, and everyone is expecting him to be close. Certainly he will want to come in there and be a success like he has been in the past. I don't think he will accept anything less, so we expect Chelsea to be there or thereabouts as well."
