England striker Kane has been out of action since September 18 after damaging knee ligaments in the victory over Sunderland but is now on the verge of returning to action sooner than expected.
The 23-year-old was expected to be out until the start of November but could make his return at the weekend at Bournemouth, boss Mauricio Pochettino saying Tuesday's Champions League clash with Bayer Leverkusen will come too soon.
"Hopefully as soon as possible we can recover him, and the team will get stronger," Pochettino said. "The Champions League game on Tuesday is too soon for him but maybe Monday he will start to train on the pitch."
Meanwhile, Spurs are positive Alderweireld's knee injury will not keep him out for months after he underwent a scan to determine the extent of the problem the Belgian picked up in Saturday's draw at West Brom.
Pochettino is hopeful the injury will not keep Alderweireld long-term and says in the meantime he is happy to play Eric Dier at centre-half, alongside Jan Vertonghen.
"The good thing about Eric is he can play like a midfielder and a centre-back, and can perform good in several positions," Pochettino said. "That is important and we will see about the decision for Tuesday. It is one option more that we have."