The Manchester City player sustained damaged ankle ligaments on club duty against Tottenham on May 5 and the injury put his prospects of playing for his country this summer in jeopardy.
He will see a specialist on Monday, and the outcome is set to determine whether Barry can be selected in Fabio Capello's 23-man finals squad.
Barry has been a mainstay of the England team during Capello's tenure and his absence could be keenly felt should he have to stay at home.
Barry told The Guardian: "I'm still feeling positive."
However he stressed: "It's too early to assess just yet whether I'll make it."
The 29-year-old former Aston Villa captain gives England the midfield balance they have lacked in recent tournaments, with his defensive qualities allowing Steven Gerrard and Frank Lampard to push forward.
In his absence, England have experimented with various formations at their training camp in Irdning, Austria. It has been reported that Gerrard was yesterday pushed into an attacking role in support of striker Wayne Rooney, with James Milner featuring alongside Lampard in central midfield during a training session.
Capello will look at all available options but would ideally be able to call on Barry.
Barry is now hoping his specialist gives him the all-clear, allowing him to make the cut for the tournament.
Barry was picked in England's Euro 2000 squad but did not get off the bench, however it would be a different story if he is passed fit this time.
"I've stayed in Manchester and worked closely with the fitness coaches at the club," Barry said.
"There had been a little confusion when it was thought I was only seeing the specialist on 29 May - a day before we play Japan in our last friendly.
"But I called the manager (Capello) and explained that the actual date is 24 May. So he was able to include me in the provisional squad and I've done everything I can - like sleeping in an oxygen tent to speed up the recovery. I'm hopeful I'll get the all-clear, even though I'll be crossing my fingers."