The West Ham United man was in fine form on Saturday afternoon as he scored a hat-trick in the 3-3 draw with Arsenal.
There is now a debate about whether he should be in England’s squad for the tournament, with the argument being that the current line-up does not have anyone who is as good as he is in the air.
Savage agrees with that idea, saying Carroll offers something different, and believing Liverpool striker Daniel Sturridge would be the one to miss out for him.
“If he stays fit he is something different off of the bench,” he told BBC Radio 5 Live 606.
“I wouldn’t start him at all but I’d have him on the bench. I would go, Harry Kane, Jamie Vardy, Wayne Rooney.
“And then I think Roy Hodgson will take Danny Welbeck because he can play him out wide. So no Daniel Sturridge, no Theo Walcott, take Carroll.”
There is no denying the West Ham star offers something different to what England have at present.
However, his game is very much reliant upon the team getting balls into the box, as West Ham did against Arsenal, and it is questionable whether England would want to play that way.
Roy Hodgson is well known for having his favourites as well, which the likes of Welbeck and Sturridge appear to be, further lessening Carroll's chances of a call-up.