But the versatility of two of their clubmates means that both are in line to miss out, according to Ashton.
It is claimed that Hodgson is considering taking three centre-backs to France, with Spurs' Eric Dier able to play there if required.
Chris Smalling, Gary Cahill and John Stones - Jagielka's defensive partner at Everton - are all said to be ahead of the 33-year-old in Hodgson's thoughts.
And Stones' ability to play right-back could convince the England head coach to leave Walker at home, with Liverpool's Nathaniel Clyne his first choice in that position.
Hodgson has an attacking dilemma on his hands, with Wayne Rooney, Harry Kane, Jamie Vardy, Daniel Sturridge, Danny Welbeck and Theo Walcott all seeking spots in his 23.
And midfield places may also be in short supply if Jack Wilshere returns to fitness in time.