Dele Alli missed training on Tuesday to have a scan on the thigh injury that limited him in England's 2-1 win over Tunisia, sources have confirmed to ESPN FC.
The Tottenham Hotspur midfielder picked up the problem during the first half in Volgograd, Russia, but remained on the pitch until he was replaced by Chelsea youngster Ruben Loftus-Cheek in the 80th minute despite visibly being inhibited in his movements.
A 91st-minute header from Harry Kane earned England their first victory in the opening match of a major tournament since 2006 after Ferjani Sassi's penalty cancelled out Kane's opener.
"We had to keep monitoring Dele," Southgate said after the game. "He was feeling a little bit of an issue just before half-time, but he felt he could carry on and I thought the runs that he was making and the way he was pressing the ball was still causing a problem.
"He had a half chance with a lovely ball Jordan Henderson played to him, lofted over the top. But we have good options on the bench, and we felt to put the freshness of Marcus [Rashford] and Ruben would both bring fresh energy but also a different sort threat to the one that we'd posed."
Any injury could threaten Alli's chances of being fit in time for England's second match in Group G against Panama in Nizhny Novgorod on Sunday.