The Everton midfielder struggled for his best form this past season.
Roy Hodgson named a 26-man provisional squad for the tournament last week, with that squad to be cut to 23 at the end of the month.
Who the England boss decides to cut from his current group remains to be seen, with the decision likely to prove a tough one.
England manager Roy Hodgson
Fabian Delph looks set to miss out after picking up an injury, but beyond him it is hard to see which other two players will be left behind.
One man who is struggling for his best form is Everton’s Ross Barkley, and Wright has suggested that he could be one of those who is cut.
“Somebody who has slipped under the radar is Ross Barkley,” he told ITV Sport.
“If they [England] are thinking of freeing up another space, then you have to look a Ross and think about how things are going for him.”
England's Marcus Rashford is substituted by Ross Barkley
It will certainly be interested to see who Hodgson decides to drop from the current selection given they have all arguably earned a place.
Manchester United youngster Marcus Rashford would have been the pick for many, but his goalscoring debut against Australia, and fine form in general, is sure to have changed that viewpoint.
England's Marcus Rashford applauds fans as he is substituted off for Ross Barkley (not pictured)