Several members of the Three Lions squad complained of minor injuries at the end of their gruelling showdown with Colombia in the quarter-finals, which went the whole way.
England were pegged back 1-1 late on in Moscow, before coming out on top on penalties to set up Saturday's meeting with Sweden for a place in the final four.
Sky Sports News reports that Alli is once again struggling with a thigh injury, which saw him miss his side's last two group games, while Kane has a problem with his back.
"It's like a scene from MASH in the dressing room," he told reporters. "Some just cramp, and some need just a little bit more assessment, so we'll know more over the next 36 hours.
"I thought there were many, many fouls in the game and I don't think we conceded anywhere near the number of our opponents."