The defender has not turned out for the Blues since suffering a hamstring strain in February, and Hodgson is keen to keep a close eye on his recovery.
"The two medical departments have been in constant touch - on Wednesday we had people from the FA here," the Daily Star quotes Everton manager Roberto Martinez as saying.
"There is no pressure to play him or not. They have been very supportive and all they want is to be informed really. They are well aware we are trying to ensure Phil doesn't get a 1% risk of an injury on the football pitch."
Jagielka may not feature in Everton's three remaining fixtures this season.