The Manchester United defender missed the Three Lions’ final training session before the friendly with Iceland on Friday as he struggles to recover from a muscle injury.
Gareth Southgate must name his final 26-man squad for the tournament by midnight on Friday and with Maguire unable to prove his fitness by then, his place is in doubt.
The Telegraph report sources close to Maguire fear he might not make the cut, although it would be a huge blow to Southgate to leave one of his most experienced and trusted players behind.
Maguire has been out of action since Manchester United’s 1-1 draw with Burnley on 27 April, missing the FA Cup final due to the injury that is still keeping him sidelined.
Southgate named a 33-man squad ahead of Monday’s friendly win over Bosnia-Herzegovina and has already trimmed it by two ahead of Friday’s meeting with Iceland at Wembley.
Tottenham’s James Maddison and Liverpool’s Curtis Jones have already departed, with five more names to be confirmed as axed by the end of Friday.
A statement from the England team on Thursday read: ‘There will be 27 players involved in today’s training session, with Lewis Dunk, Harry Maguire and Luke Shaw following individual programmes.
‘James Maddison and Curtis Jones have departed the England camp, having been told they are not part of our final EURO 2024 squad.
‘We thank them for being an important part of our pre-tournament preparation.’
Southgate is not short of options at centre-back if Maguire does miss out, with John Stones, Marc Guehi, Lewis Dunk, Ezri Konsa, Joe Gomez and Jarrad Branthwaite all in the current squad.
Liverpool’s Jarell Quansah is also with the England camp but is expected to be cut ahead of the trimmed down 26-man squad being confirmed, ahead of England’s first group game next Sunday.
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