But former Liverpool striker Saunders reckons Jurgen Klopp could snatch the France international away from the clutches of United.
He will have a conversation with them if he's coming to England.
Dean Saunders on Antoine Griezmann potentially joining Liverpool.
He told LFC TV: "I mentioned Griezmann and Liverpool will be on his list now.
"He will have a conversation with them if he's coming to England."
Jurgen Klopp admitted last week that hopes of securing top transfer targets will increase with Champions League football.
And the Reds guaranteed their return to Europe's elite competition after beating Middlesbrough 3-0 to pip Arsenal to the fourth and final qualification spot.
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Dean Saunders reckons Liverpool are in with a chance of signing Antoine Griezmann
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The German boss spoke with the Liverpool sporting director Michael Edwards yesterday to outline transfer plans for the summer.
And Klopp could now fancy his chances to land a high calibre signing like Griezmann with chiefs willing to hand him more than £100m to bring in new recruits.
However, Manchester United will boost their chances of signing Greizmann even more if they beat Ajax in the Europa League final on Wednesday (7.45pm) as they will secure Champions League football themselves for next season.
Griezmann has made 53 appearances for Atletico this season and has scored 26 goals.