The Red Devils have been heavily linked with a move for the France international since Jose Mourinho’s appointment as Louis van Gaal’s successor last summer.
Griezmann has consistently been one of Europe’s most-prolific goal-scorers during the forward’s four-year stay at Diego Simeone’s Atletico Madrid.
The Independent reported last month that Manchester United remain keen to sign the 25-year-old as Mourinho looks to bolster his forward options ahead of his second season at Old Trafford.
Speaking to BBC Radio Five Live’s 606 podcast after the Red Devils played out a frustrating 1-1 draw with 10-man Bournemouth on Saturday afternoon, Savage was asked whether Manchester United would sign Griezmann.
Savage said: “I think they will – yes.”
Manchester United signed four players in the summer transfer window following Mourinho’s appointment as manager last year.
Zlatan Ibrahimovic has scored 15 times in 25 games in the Premier League in the 2016-17 season.
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