Atletico Madrid's hitman netted again on Tuesday night, scoring in their 4-2 Champions League triumph away at Bayer Leverkusen.
The France international has continually shown prolific form for club and country on the back of an outstanding tournament at Euro 2016.
Antoine Griezmann has four goals in Atletico Madrid's last four Champions League games
The 25-year-old has outlined he is happy at Atletico and determined to achieve success there.
But a big-money switch to Manchester United is backed by Keane who would welcome Griezmann's talent at Old Trafford.
"He's been fantastic," Keane said on ITV's Champions League highlights show.
Antoine Griezmann is eyeing Champions League glory with Atletico Madrid following Tuesday's win
How Man United could look with Antoine Griezmann
Wed, February 1, 2017
Is this how Manchester United's squad could look with Antoine Griezmann
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Is this how Manchester United could look with Antoine Griezmann
Roy Keane is very keen to see Antoine Griezmann join Manchester United
What a player he'd be for United
"I've been really shocked at the level he's been playing at over the last two or three years, he's been fantastic.
"We're seeing the goals now on a regular basis in all the big games, at international level, the big Champions League nights.
"Really top player, and obviously he's been linked with Man United.
"What a player he'd be for United."