The Old Trafford greats see the 26-year-old as the natural successor to Paul Scholes, who hung up his boots for the second time at the end of last season.
New Red Devils boss David Moyes has been heavily linked with a move for Fabregas, with speculation suggesting he could leave Camp Nou and return to the Premier League during the current transfer window.
"I think [Cesc] Fabregas is a fantastic player and I hope he's playing for Manchester United next season," Robson enthused.
Central midfield has been identified as the area the reigning champions must strengthen as a priority, with Manchester United heading into 2013/14 a little short on options.
Fabregas would obviously add even more quality to the first-team squad that Moyes inherited from Sir Alex Ferguson. But, Yorke also highlighted the possible reunion between the Spain international and Robin van Persie as a prospect to get excited about.
"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."