Griezmann has scored 25 goals for Atletico Madrid this season, and has been linked with a move to a host of clubs in the summer as a result. United appear to be frontrunners to secure the France international's signature, however, after Griezmann's advisor admitted United were the first club to make contact over his client's availability.
Image:Zlatan Ibrahimovic injured his knee after landing awkwardly in last week's win over Anderlecht
And with Wayne Rooney reportedly set to depart the club at the end of the season, Wilkins hopes United can lure Griezmann to Old Trafford to bolster their attacking options, but feels Champions League football could be a necessity in order to land the in-demand striker.
"I think United have always had these really sharp centre forwards that poach goals like Dwight Yorke and Andy Cole and Griezmann is exactly that type of player," Wilkins told Premier League Daily on Sky Sports News HQ.
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"So as far as United are concerned I'm sure they would love him, but at the end of the day, if you finish outside of the Champions League places - and this applies to Manchester City as well - bringing players in of that quality is almost impossible.
"[Paul] Pogba did it. Pogba came back to Old Trafford without a year of Champions League football. Will he regret his move? I don't know because the Champions League is where these guys want to play and at the moment it's in the balance."
Image:Griezmann was top scorer at Euro 2016
Wilkins described Jose Mourinho's signing of Ibrahimovic, who turns 36 in October, as "a masterstroke" and said the striker's sheer presence inspires his team-mates.
United have not revealed the full extent of Ibrahimovic's injury, but leading Swedish sports therapist Sharon Heidaripour has no doubt her compatriot can make a swift recovery.
Speaking at Kick It Out's Raise Your Game conference, Heidaripour told Sky Sports News HQ: "There are four ligaments in the knee and, depending on which ligament is damaged, it can take up to nine months unless it's a cruciate ligament injury with further damage in the knee joint, which would take a little longer.
Image:Sports therapist Sharon Heidaripour has also worked with FIFA
"But having followed Zlatan's career closely, he has always been a very strong character so I think he has every chance of returning from the injury quicker than a lot of other players. Mentally and physically Zlatan is a lion - as we have seen this season - so that will help him come back quickly.
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"I think his age will act as a driver for him. People talked a lot about his age when he came to the Premier League, so I don't think that will matter much. The healing process will take its time but mentally Zlatan has no issues."
