Damage to ligaments in his right ankle has seen Kane sidelined for just over six weeks
Damage to ligaments in his right ankle has seen Kane sidelined for just over six weeks but he did take a reduced role in first-team training on Monday and Tuesday.
He is due to be involved in full training on Thursday and could now feature in Sunday's derby clash at Arsenal's Emirates Stadium.
When asked on Tuesday about the 23-year-old Kane's prospects, Spurs boss Mauricio Pochettino said: "Tomorrow (Wednesday), no, not on the bench.
"It's good because you can see him today warming up with the team to be involved in some exercises. But no, for tomorrow he is not ready.
"Sunday? Maybe, maybe."
Spurs defender Toby Alderweireld is still out of action with a leg injury, while Erik Lamela remains doubtful to face Leverkusen because of a hip problem.
Should Kane feature in some capacity against Arsenal it would bolster his chances of being called up for England duty later this month.
England face old rivals Scotland in a 2018 World Cup qualifier at Wembley on November 11, four days before a home friendly against Spain.
While some in the Spurs' hierarchy might prefer it if Kane were spared England appearances so soon after an injury lay-off, Pochettino said he will not stand in his way if he is selected by England interim manager Gareth Southgate.
"If he is available to play Sunday against Arsenal then it will be difficult for us to stop him if the national team call him," Pochettino said.
"We are pro-national team always for all the players. If Harry is available we are not stupid to say 'no, Harry is out,' to try to protect him so that after two weeks he can be with us.
"We want the best for the team and for the player. It's true that maybe it makes more sense for the national team to say: 'Okay, stay at home. Stay with Tottenham and train for two weeks. It's important to build Harry's fitness and be better after'.
"But, if they consider that they need Harry to play for the national team and he is available to play against Arsenal then we cannot stop."
Tottenham may be the only unbeaten team left in this season's Premier League but they have not won any of their last five matches in all competitions and have not scored in open play in their last four fixtures.
German club Leverkusen are third in Group E, just a point behind Spurs, and Pochettino said: "It's important to win. Leverkusen is a very good team with very good players. I think it will be tough.
"We need to be more clinical in our offensive situation. We need to be determined and aggressive in the last third," the Argentinian added.