England's Ben Chilwell and Mason Mount are doubts for Tuesday's game with the Czech Republic as they self-isolate as a precaution after coming into close contact with Scotland's Billy Gilmour.
The pair were seen interacting with Chelsea team-mate Gilmour after Friday's draw with Scotland at Wembley.
Gilmour has since tested positive for Covid-19 and will miss Scotland's final group game against Croatia on Tuesday.
"I can't say it isn't disruptive," said England boss Gareth Southgate.
Speaking on Monday evening about whether the pair would be available for Tuesday's game at Wembley, he told BBC Radio 5 live: "You would have to say at this moment in time they are a big doubt for tomorrow.
"The worst-case scenario would be that the two boys would be out for 10 days from the game last Friday."
Chilwell and Mount were seen hugging and speaking to Gilmour after the final whistle of Friday's game.
Public Health England (PHE) guidance states that someone could be considered a close contact and might have to self-isolate if they had a face-to-face conversation within one metre, or had been within two metres of someone for more than 15 minutes who tested positive for Covid-19.
A PHE spokesperson said: "PHE is working with the FA to identify close contacts of Billy Gilmour and any risk to other players and staff."
The Scottish FA (SFA) says PHE deemed that none of the other Scotland players had to self-isolate as there had been no close contact.
But PHE said there had been no detailed discussions with the SFA.
While it can advise, it is understood PHE believes any decision to tell players from the England team to isolate will have been made by the FA.
The entire England squad had lateral flow tests on Monday afternoon and all were negative.
In a statement, the FA said it would hold further talks with PHE before taking further action.
"The pair will be kept away from the rest of the England players and wider support team, pending further discussions with PHE," read the statement.
"We will continue to follow all Covid-19 protocols and the Uefa testing regime, while remaining in close contact with PHE."
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