The forward missed Tottenham Hotspur's clash with Manchester United towards the end of last month with a hamstring problem, while he had to be substituted in the second half of Sunday's clash with Crystal Palace after a heavy challenge from Timothy Fosu-Mensah.
Kane is in line to feature for England against Germany and Brazil on November 10 and November 14 respectively, but the 24-year-old has conceded that his fitness will have to be monitored over the next few days.
"The knock in the first half was still niggling. It was a sore one. The manager makes the decisions for the team and he obviously thought that was the best decision," Kane told reporters.
"The hamstrings are fine but look, we've got keep an eye on it. It's something that happened and we don't want it to happen again. It's about maintaining it, it's a long old season so we go away now and we do a bit of work and hopefully get ready for Friday.
"We play so many games and we've had so many high intensity games – United, Madrid, Liverpool – it takes it out of you. The manager does his best here to keep everyone in the best shape possible and I'm sure Gareth [Southgate] will do the same.
"Gareth will make the decision based on what he thinks is best for the players and the team. If I'm fit and called upon I'm happy to play. It's always an honour to play for my country, I'd never turn that down."
Should Kane be passed fit, he is expected to wear the captain's armband against Germany on Friday night.