Kane has been out for just over six weeks after injuring ligaments in his right ankle but the 23-year-old was involved in first-team training both on Monday and Tuesday.
He only did half-sessions with the rest of the squad, however, before separately completing a specific recovery programme on his own. Kane is expected to take part in full training again tomorrow.
Mauricio Pochettino said his top striker will not feature against Leverkusen at Wembley tonight but left open the possibility of a north London derby return at the Emirates Stadium this weekend.
“No, not on the bench,” Pochettino said. “It’s good because you can see him today warming up with the team to be involved in some exercises. But no, he is not ready. Sunday? Maybe, maybe.”
Toby Alderweireld has also missed the last four matches with a leg injury and Pochettino appeared less optimistic about the defender’s chances of featuring this week.
Pochettino at one stage hoped Alderweireld would play against Leicester last Saturday but the Argentinian admits there have been some “slight problems” with his rehabilitation.
The Belgian was seen stretching on his own in the gym at Tottenham’s training ground on Tuesday before later completing some sprint exercises separately from the rest of the squad. Erik Lamela has recovered from the illness that kept him out of the squad against Leicester but is still a doubt to face Leverkusen after feeling a problem in his hip yesterday.
Kane’s comeback will be a timely boost for Tottenham. Spurs have failed to score from open play in their last four matches and cannot afford a slip-up against Leverkusen, who sit third and only a point behind them in Group E.
“It’s important to win. Leverkusen is a very good team with very good players. I think it will be tough,” Pochettino said. We need to be more clinical in our offensive situation. We need to be determined and aggressive in the last third.
“It’s true that the last few weeks after the international break it was difficult for us to score. We are creating the same chances as before.
“But it’s true that our percentage was poor in front of goal. We are working on that.”
Meanwhile Bayer Leverkusen striker Javier Hernandez insists he has nothing to prove to English football as his goal record at Manchester United speaks for itself.
The Mexican left the Premier League with an impressive strike rate of 37 goals in 103 matches - almost one every 130 minutes - and has proven his class in Germany, scoring 26 times in 40 appearances last season. This term he already has seven in 13. Asked if he had a point to prove against Spurs, Hernandez said: “No, definitely not. Any minutes I had on the pitch at Manchester United I tried to do my best. Thankfully the numbers are positive for me. When I left I had the fourth (best) record in history of minutes and goals in the Premier League. That’s what I had at United.”
Leverkusen, who sit third and a point behind Spurs in the group, will be without their captain Lars Bender as he is suffering from a heel problem.