The Tottenham midfielder picked up a thigh strain in the opening game against Tunisia on Monday, leading the England medical team to keep a close eye on him this week.
A scan appeared to show that the damage was not severe enough to end his tournament prematurely, but it remains to be seen if he will play any part against Panama.
A seemingly leaked teamsheet on Thursday appeared to suggest that Alli would play no part in Sunday's game, with Ruben Loftus-Cheek coming in for him and Marcus Rashford replacing Raheem Sterling.
England will undertake their final training session on Friday before they make the trip to Nizhny Novgorod for the game, with Alli not expected to be involved if he misses out.
However, with that session set to involve detailed work on tactics and shape it is closed to the public, meaning fans may not discover about Alli's fitness until the teams are named for the game.