Despite that, Southgate has revealed Kane will start on Tuesday night with England needing to beat the Czech Republic if they are to advance as winners of Group D.
“You can assume that, yes, absolutely,” Southgate replied when asked if Kane would keep his place.
“He is fundamental not only to the goals he scores but the build-up play and everything else he brings.”
There was a clamour among fans for Jack Grealish against Scotland, with loud cheers when the Aston Villa captain came on in the second half.
With Phil Foden facing a suspension if he is booked, Southgate may be tempted to drop the Man City star and play Grealish instead.
In defence, Southgate could once again rotate his full-backs, while Harry Maguire is pushing for a start – but successive clean sheets mean Tyrone Mings and John Stones could continue at centre-back.
Czech Republic vs England predicted lineups
Czech Republic XI: Vaclik; Coufal, Celustka, Kalas, Boril; Soucek, Holes; Masopust, Darida, Jankto; Schick
England XI: Pickford; James, Stones, Mings, Trippier; Phillips, Rice; Grealish, Mount, Sterling; Kane
Boril, Hlozek, Masopust (Czech Republic) and Foden (England) will miss the next game if they are booked.
Goalkeepers: Tomas Vaclik, Tomas Koubek, Ales Mandous
Defenders: Jan Boril, Jakub Brabec, Vladimir Coufal, Ondrej Celustka, Pavel Kaderabek, Tomas Kalas, Ales Mateju, David Zima
Midfielders: Antonin Barak, Vladimir Darida, Adam Hlozek, Tomas Holes, Jakub Jankto, Alex Kral, Lukas Masopust, Jakub Pesek, Tomas Soucek, Petr Sevcik, Michal Sadilek
Forwards: Michael Krmencik, Tomas Pekhart, Patrik Schick, Matej Vydra
Goalkeepers: Sam Johnstone, Jordan Pickford, Aaron Ramsdale*
Defenders: Ben Chilwell, Conor Coady, Reece James, Harry Maguire, Tyrone Mings, Luke Shaw, John Stones, Kieran Trippier, Kyle Walker, Ben White
Midfielders: Jude Bellingham, Jordan Henderson, Mason Mount, Kalvin Phillips, Declan Rice
Forwards: Dominic Calvert-Lewin, Phil Foden, Jack Grealish, Harry Kane, Marcus Rashford, Bukayo Saka, Jadon Sancho, Raheem Sterling
* Replaces Dean Henderson, who withdrew due to injury