The 31-year-old - who sat out October's 2-1 defeat to the Pirate Ship on account of a minor injury - recently slammed his international teammates who pulled out of Lee Carsley's squad for November's matches.
As many as eight players withdrew from the original selection, and one of the five replacements called up - Everton's Jarrad Branthwaite - also pulled out ahead of the clash with Greece this week.
Kane expressed his belief that clubs are taking "advantage" of the situation with the England team, as Carsley will only be in charge for two more matches before stepping aside for Thomas Tuchel in the New Year.
The former Tottenham Hotspur man would have been expected to spearhead the attack for Thursday's match, but according to journalist Sami Mokbel, he is nursing a niggle and is not certain to feature.
Who could start instead of Kane for England?
There is still a chance that Kane could shake off his concern in time for the pivotal contest, as anything other than victory for England will extinguish their hopes of automatic promotion to League A.
However, Mokbel reports that Ollie Watkins is currently 'on standby' to replace his skipper if needs be, with the Aston Villa man seemingly ahead of Dominic Solanke in the Three Lions' pecking order.
Watkins set up goals off the bench in both of England's matches against Greece and Finland last month, and he will be making just his sixth start for the national team should he step in for Kane this evening.
West Ham United's Jarrod Bowen is an alternative option in the centre-forward role for England, who sit three points adrift of Greece in League B Group 2 of the Nations League.
As head-to-head records take precedence over goal difference in the Nations League, the Three Lions will not be able to overtake Greece on the final matchday if they come away from Athens with a point.
Timing of Kane injury ironic after England comments
As the England captain, Kane was never going to come out and say that club football is more important than representing the national team, but the timing of this 'niggle' could hardly be more ironic.
The immediate replies to Mokbel's post were scathing and sarcastic in nature, with one user on X posting: "He should play. Country over any injury," after the striker's stern words to his teammates who had pulled out.
Eight withdrawals in one go is certainly unprecedented, and one cannot help but wonder whether clubs would have pulled so many players from the selection had Tuchel already taken the reins or Gareth Southgate still been at the helm.
Genuine injuries are more than a good enough excuse to pull out, though, and teams competing in Europe have also had extra games added to an already unforgiving schedule thanks to the expansion of UEFA club competitions.
Kane will also have the luxury of a Bundesliga Christmas break between December 20 and January 11, but there will be four rounds of Premier League fixtures in between those dates, as well as the EFL Cup quarter-finals next month.