The West Ham United striker has proved a useful impact player this season.
Carroll scored in the Three Lions' 3-2 win against Sweden at the last Euros in Poland and Ukraine, and has proved a useful option from the bench this season - scoring three of his four Premier League goals off the bench.
But Wright, an ex-Hammers striker himself, can't see the Geordie front man forcing his way into Roy Hodgson's plans.
Responding to a caller on BBC Radio Five Live's 606 phone-in on Sunday, the 52-year-old said: "I've seen Barcelona do it with (defender, Gerard) Pique, throw him up there when the game's running away from them, but I'm not sure at this particular time if that's going to be something that Roy Hodgson is going to be looking at.
"Although we know that it works and it will continue to work until the end of time, if you get a big man up there and he's capable enough and he can knock it down for runners... people do it at the end of the game when they're getting desperate.
"But he's going have to use up a spot to bring Andy Carroll as maybe a substitute, and I think that might be too much for him."
Hodgson has a wealth of striking options available to him at present, with Harry Kane and Jamie Vardy staking their claims for starting places by scoring in Saturday's friendly win against Germany.
Danny Welbeck was replaced by Vardy in Berlin, with Daniel Sturridge and Theo Walcott making up England's current striking pool.
And Wayne Rooney, who captains the Three Lions when fit and is the country's all-time leading scorer, will surely have returned to contention by the start of the tournament in June.