The Liverpool full-back limped off during England's 1-0 friendly win over Austria with manager Gareth Southgate admitting that it was "not a good sign" for the player's chance of making an impact at the tournament.
The Three Lions boss told Sky Sports: We've got to see, it's obviously not a good sign that he's had to walk off the pitch, and he was in some discomfort.
"We're so close to the finals that for any player, injuries make them a doubt. But we will just have to see over the next 48 hours."
Asked if another player would be called up if Alexander-Arnold was absent, Southgate said: "Let's see how Trent is first then we'll go from there."
Meanwhile, Southgate also played down fitness concerns surrounding Jack Grealish and Jordan Henderson with just 10 days until England's opener against Croatia.
He said: "With Jack, we just felt that that was enough time.
"I think you can see still a little bit of sharpness still coming and we didn't want to overplay him through that period.
"With Jordan, we had hoped to involve him today. That was the original plan. This morning he wasn't so happy with how he felt.
"We've scanned him just to be certain. There's no problem on the scan so he'll be able to resume training but we've taken a decision to leave him out of this game."