United and City are monitoring events, with Griezmann finding himself at odds with captain Lionel Messi and frozen out by coach Quique Setien.
Having been signed from Atletico Madrid for €120m last summer, Griezmann's first season at the Nou Camp has not lived up to expectations.
Both the father and brother of Griezmann has hit out at Setien after Tuesday night's 2-2 draw with Atletico Madrid. Setien came underfire after putting Griezmann on against his old club in the 91st minute.
And watching closely are both Manchester giants ahead of the summer market.