The towering West Ham striker appears to be back to his best, and his physical abilities make him a different threat that any of the other players Roy Hodgson can call upon.
However, there are a number of strikers ahead of Carroll in the pecking order, including the Harry Kane, Jamie Vardy, Wayne Rooney and Danny Welbeck.
Daniel Sturridge is also under consideration by Hodgson, but Winstone believes Carroll should be ahead of the Liverpool striker, who, in his opinion, ‘is not a great finisher’.
When asked if he’d take Carroll to the Euros, the 59-year-old told the Alan Brazil Sports Breakfast: “Yes I would. My forward line would be Harry Kane and [Jamie] Vardy.
“I’d take two forwards, and obviously take a winger, you have to have pace.
“Just as a keepsake, for when you are 1-0 down with 20 minutes to go, there is no-one in Europe that would be ready to play Andy Carroll. There’s just not those centre forwards about.
“You bring in one and he’ll liven them right up. So I’d definitely bring him – not just because I am a West Ham fan. I just think he’s a bit of a secret weapon they wouldn’t know much about.
“And the Liverpool kid [Daniel Sturridge] is not a great finisher! He could be [a top striker], but the finishing is just not there for me.
“Vardy and Kane – Kane’s an incredible finisher and [both] have got to start.
“I’d love to see us go there and really have a go. I think Roy has been brave up to now and used a lot of young players – as England manager I might give him a call and give him my opinion!”