The 24-year-old played in the Toffees' 3-2 victory over Watford in the Premier League on Sunday after returning from a recent leg injury.
Dele Alli is already out of England's squad after missing Tottenham's win over Crystal Palace with a hamstring injury, while his Spurs team-mates Harry Kane and Harry Winks are doubtful after picking up knocks at Wembley. England host Germany on Friday and meet Brazil four days later.
The pair required treatment during the 1-0 win over Palace, with Tottenham boss Mauricio Pochettino saying Winks, who went off at half-time, had twisted his ankle.
Chelsea centre-back Gary Cahill, who helped his side beat Manchester United on Sunday, will also be assessed by his club before joining up with the national team.
A statement on the Football Association's website confirmed Keane had been added to the group of players due to report at St George's Park later on Monday.