Ibrahimovic joined the Red Devils last summer and has gone on to make a huge impact at Old Trafford, scoring 28 goals before a knee injury brought his season to an end.
With Mourinho set to splash out on signings in the coming transfer window, Griezmann is one of the players of interest to the Portuguese manager.
According to Leon Osman, the French international would be a great addition to the squad, and could make as much of an impact as Zlatan Ibrahimovic. He told 'Premier League Daily': 'I think he would be [as big as Ibrahimovic]'.
The former Everton man had nothing but praise for the Atletico star: 'He's consistently scored goals at every level he's played at over the past number of seasons. He's helped Atletico to the titles they've won and he is one of the main people of French football'.
'Griezmann will score more goals, which is every marketing person's dream', the former England international continued, 'I think he would be a big hit for United.Will he be able to take that number seven shirt at Old Trafford, which comes with its own pressure? He seems just the right fit for the shirt. I think it would fit him really well'.
Ray Wilkins also backed the 26-year-old to be a hit if he completes the move: 'He's an exceptional footballer so anyone who gets him will be pushing for the title next year. This guy has scored goals at every level he's played and at the top level as well', said the retired Red Devil.
Antoine Griezmann could make all the difference at Old Trafford, bringing quality and pace to the attack: 'United have always been used to having centre forwards with pace. I know Ibrahimovic doesn't have it and Wayne Rooney certainly had it when he joined Manchester United', Wilkins stated, 'but now they've got that pacey attack again and he would add that little bit of quality. Where they've been drawing those games, this guy would be sticking the ball in the back of the net'.