However, ahead of Saturday's final friendly with Belgium, two other doubts, Glen Johnson (toe) and Danny Welbeck (ankle), were at least able to start training, although Hodgson had previously expressed doubt either man would be fit for his first game at Wembley.
He was eventually able to continue though and will come into contention for the Belgium game.
Hodgson must be concerned about the prospect of picking up further injuries, but with the Chelsea trio of Ashley Cole, John Terry and Gary Cahill, plus Wayne Rooney, all due a game, the England manager cannot afford to take the game lightly as his side prepare for their Group D opener with France in Donetsk on June 11.
The concern over Parker is understandable given so much now rests on him as central midfield partner for captain Steven Gerrard.
Parker may have overcome the Achilles injury that ruled him out of Tottenham's final four games.
But it has been noted the 31-year-old is operating below the levels he produced at Tottenham before the turn of the year.