The midfielder was forced off less than 30 minutes into a substitute appearance during Saturday's 1-0 friendly win over Norway, and requires a scan to determine the extent of the blow.
The scan could, however, be inconclusive, resulting in a dilemma ahead of the May 29 squad submission deadline over whether or not to select a player whose fitness is not assured.
"We only have a couple of days to sort it out and we can't take any risks," Hodgson told reporters.
|NORWAY 0-1 ENGLAND
|Hodgson impressed by England's discipline
Should the Manchester City midfielder prove too much of a risk ahead of the tournament, the manager hinted that defender Phil Jagielka could be the chosen replacement from the standby list.
With only seven recognised defenders in the squad, the Everton centre-back could get the opportunity to build on his display in November’s win against Spain and make up for missing World Cup 2010 through injury.
"I am prepared to reconfigure," Hodgson added.
"I am not necessarily looking to replace man-for-man in the midfield area because we have a lot of players in that area."
Hodgson has received no further bad injury news, however, with Scott Parker suffering no ill effects from his recent Achilles injury and both Danny Welbeck and Glen Johnson improving.
"I am not worried about Glen Johnson. I am not worried about Danny Welbeck," the England boss concluded..