Carroll has scored two goals in nine appearances for the England national team so far in his career.
The former Newcastle and Liverpool striker has struggled with injuries in recent years, but he is now fully fit and back playing Premier League football.
The 27-year-old scored a stunning hat-trick for West Ham in their 3-3 draw with Arsenal at the Boleyn Ground in the Premier League on Saturday afternoon.
While many will claim that Carroll should at least be in contention of a place in Roy Hodgson’s Three Lions’ squad, former Newcastle striker Shearer has explained why he should not be part of the team.
“I was with him at Newcastle so I know the ability he has - when he gets the right delivery he is unplayable,” the former England international striker wrote in The Sun. “But we have seen that ability for three or four games in a row before, then he goes and gets injured.
“That has always been the case with Andy and that is why, at this moment in time, he should not be considered for England. He has had one good game but plenty of other English strikers have been doing it all season and are rightly ahead of him.”
Former Liverpool defender Mark Lawrenson is also of the belief that Carroll should not be part of the England squad in the summer.
“He is way down the list of the strikers they have got,” said Lawrenson on MOTD2 Extra on Sunday afternoon (broadcast from 12:15pm, April 10) regarding Carroll’s Euro 2016 finals chances. “England have got a luxury of strikers. No way.”
Carroll has scored seven goals and created eight chances in 21 Premier League appearances for West Ham so far this season.