The Sun reports that United scout Martin Ferguson watched McGregor in action for Scotland at Hampden on Tuesday.
The 28-year-old made several stunning saves in the Euro 2012 clash with Spain.
McGregor’s contract with Rangers is set to expire in the summer of 2013.
United are looking to bring in a long-term replacement for veteran Edwin van der Sar.
The Reds Devils have also been keeping tabs on Ajax keeper Maarten Stekelenburg, Atletico Madrid’s David de Gea and Schalke No1 Manuel Neuer.
