Although Hodgson predicted a scan on the problem Barry suffered during the second-half of Saturday's 1-0 win over Norway would take place within 24 hours, it now transpires the assessment will not be made until Monday.
The chances of Barry satisfying Hodgson of his fitness before England's confirmed 23-man squad has to be submitted to UEFA on Tuesday lunchtime appear remote, although the Three Lions boss accepts he may have to take the Manchester City man on trust.
If Barry is ruled out, Liverpool's Jordan Henderson should, in theory, be the replacement as the midfield standby.
However, even though he won his third cap in the Ullevaal Stadium, Henderson has been below-par for long periods of his debut season on Merseyside and Manchester United's Michael Carrick might have been a better bet.
Hodgson has an alternative option though, especially now it seems certain both Danny Welbeck and Glen Johnson will be declared fit for this summer's finals in Poland and Ukraine after their recent scares.
Jagielka was outstanding alongside Joleon Lescott in central defence on Saturday.
It will not have gone un-noticed that Jagielka was also part of the England defence when they secured that excellent win over world champions Spain in November.
And it seems the Everton man will get the call.
"I am prepared to reconfigure," said Hodgson, when asked if he would be willing to replace a member of his midfield with an additional defender.
"I am not necessarily looking to replace man-for-man in the midfield area because we have a lot of players in that area."
James Milner proved his versatility by occupying a central midfield role against Norway, whilst Manchester United's Phil Jones has done the job for club and country.
It means England are not as vulnerable to Barry's absence as they were two years ago, when Fabio Capello selected the Manchester City man in his World Cup squad even though he was not fit enough for the opening game and failed to do himself justice even after that fateful draw with the United States.
"We only have a couple of days to sort it out and we can't take any risks," said Hodgson. "Gareth is a big man and when big men get injuries they sometimes takes a bit of time to heal.
"He is a very honest individual and whilst the scan will tell us a lot, if it doesn't give us the answer we want I shall be having a very serious discussion with him.
"He will have to be honest with me and let me know exactly how it is."
It was the same with Scott Parker following his recent Achilles problem.
The Tottenham midfielder repeatedly re-assured his manager he would recover in time and his 60-minute outing yesterday provided enough proof for Hodgson to turn an inquiry about Parker's health on its head.
"I don't understand the Parker question," he said. "I don't understand what anxiety I need to have over him.
"Every day I have asked him how he is feeling. Now he has given me the answer."
It means that Monday's medical bulletin is not being feared with quite the trepidation that might have been expected.
For, apparently, enough improvement has been shown by Welbeck and Johnson for Hodgson to allay any doubts over their involvement even if the former man in particular might not actually do any training before England depart for their base in Krakow on June 6.
"I am not worried about Glen Johnson. I am not worried about Danny Welbeck," said Hodgson. "We have sorted that one out.
"I am convinced they will be more than fit when they get on the plane to go to Poland."
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