Having already seen Frank Lampard and Gareth Barry sidelined by injury, England can ill afford to lose another midfielder but Hodgson has eased concerns about Parker.
There had been serious doubts about the 31-year-old's form heading into the Euros after he missed Tottenham's final four games with an Achilles injury.
However, when asked if he has any ongoing concerns about Parker's overall fitness, Hodgson said today: "No, not particularly, no more so than the obvious one that we were going to have, that when he came to join us having not played for Tottenham in the last two or three matches in the league.
"So that was obviously going to be a factor, but we also knew we had lots of training time and now in the two weeks we've been training he's taken part in every training session and he's also played 60 minutes already and he's available to play tomorrow.
"So he'll be getting fitter by the day, as will Wayne Rooney, and we're quite happy that by the time we play France people will be in good physical shape."
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