The ex-Arsenal captain completed his return to the Premier League ahead of the World Cup earlier this summer, switching from Barcelona to the Blues in a deal worth around £27m.
United were linked with Fabregas in 2013, but a botched transfer window under David Moyes saw the Old Trafford side miss out on the playmaker.
There was talk that the club would return for the 27-year-old this time around, but in what has been another frustrating window they have signed only three players – Marcos Rojo, Luke Shaw and Ander Herrera.
McGrath – who played the Theatre of Dreams between 1982-1989 – believes that had United made a serious move for the silky star he would be wearing a red shirt and not a blue one this season:
“I’m sure Cesc Fabregas would have picked Man United [over Chelsea] simply because of the history.” He told talkSPORT.
“Most people believe that United is the bigger club, with the history and everything else,
“It is amazing we can’t get these players. I think it is a lack of leadership on the Manchester United side. The club doesn’t need selling because people want to play for them but it is going out there, getting those players, and doing it quick.”