The 21-year-old has shone for his side in the Europa League, while also impressing for the England Under-21 team.
He may very well get his chance against Newcastle United later today, though, after scoring a hat-trick against Asteras Tripolis in Europe on Thursday night.
Intriguingly, Kane offered to go in goal to replace Hugo Lloris after netting his hat-trick, as the shot stopper had been sent off.
The Three Lions are set to face Slovenia in a Euro 2016 qualifier, as well as Scotland in a friendly.
Walker is believed to be in the frame for the national squad for those fixtures, despite having not played a game for Spurs in seven months due to injury.
Hodgson will check on the 24-year-old's fitness first, however, although his eagerness to include him suggests a lack of faith in his current options at right-back.