As per BBC Sport, the club were considering activating the Frenchman's 100 million Euro escape clause this summer, however a source close to the deal states Griezmann is no longer a priority.
The news comes as Los Coloncheros lose their appeal against their transfer ban, which prevents Diego Simeone's side from bringing anyone into the club until January 1 2018, after the Court of Arbitration for Sport upheld their complaint.
Jose seeks reinforcements
As the Red Devils look to fight for trophies next season on multiple fronts - including a return to the Champions League - United have been tracking the French international striker for a number of months.
With talisman Zlatan Ibrahimovic recovering from an ACL injury and with the Swede's future in England shrouded in doubt, Mourinho had earmarked Griezmann to spearhead his front line.
Now however, the Portuguese is set to turn his sights elsewhere.
During the past week, United have been linked with a move for Inter Milan winger Ivan Perisic, but the club have yet to make an official move for the Croatian, whilst a move for Everton striker Romelu Lukaku is being touted.
Atleti to hold on to their mann?
With reports Alexandre Lacazette was set to switch Lyon for Madrid in the close season, CAS' decision has thrown the move into doubt, at least temporarily.
With Fernando Torres also existing as Simeone's sole option up front until the winter transfer window opens for registration, Atleti could find themselves short up front for the first half of the season should they opt to cash in on their star striker.
Griezmann has scored 60 goals in 111 appearances for the Madrid club.