The former Arsenal and Crystal Palace striker was speaking after Friday night’s 2-1 friendly win over Australia at Sunderland’s Stadium of Light.
And the 52-year-old believes Toffees midfielder Barkley’s hopes of appearing at another tournament for England could be dashed if manager Roy Hodgson plumps for other options in his squad.
“Somebody who has slipped under the radar is Ross Barkley,” Wright said.
“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.”
Barkley endured a mixed campaign for the Blues last term – starting in impressive form before falling away in the last couple of months as the team struggled for form and results.
The 22-year-old was included in manager Roy Hodgson’s provisional 26-man party ahead of this summer’s international tournament in France, but has not been included in the starting line-up for the recent friendly victories over Turkey and Australia.
Hodgson must reduce his squad by three players by 11pm on Tuesday, before one final friendly match against Portugal ahead of their Group B opener against Russia on June 11.
Manchester City midfielder Fabien Delph’s hopes have already been dashed due to a calf injury, while Liverpool and Manchester United strikers Daniel Sturridge and Marcus Rashford are thought to be vying for the final forward option in Hodgson’s squad.
If the 68-year-old decides to take both forwards, however, Barkley’s position could be in jeopardy.
Barkley has 21 caps for England’s senior national side, and has scored two goals for the Three Lions.
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