Kane suffered the injury in the League quarter-final first leg against Manchester City on April 9 and has been unavailable since.
The England forward clashed with Fabian Delph as he attempted to close down his international team-mate, with the Spurs man coming off worse as he was forced off the pitch and has subsequently missed the last eight matches.
It was suggested by Mauricio Pochettino at the time he could be unable to feature again this season, bringing an end to a campaign that had seen him score 24 goals in all competitions.
But Spurs' remarkable run in the Champions League, culminating in their elimination of Ajax on away goals after a 3-3 aggregate draw in the semi-final, has prolonged the club's season by almost three weeks.
That victory over the Dutch side means they've set up a final meeting with Liverpool on June 1, giving Kane plenty of time to try and get himself fit and available for the match in Madrid.
Indeed, during Spurs's celebrations in Amsterdam, Kane was seen running on to the pitch to join the rest of his team-mates, suggesting his condition has improved significantly.
And ahead of Tottenham's final Premier League game of the season against Everton on Sunday, the club confirmed Kane has returned to the training pitch.
However, he is not expected to play any part for the Toffees' visit, which Heung-Min Son and Juan Foyth will also miss due to suspension having been sent off last time out in the 1-0 loss ot Bournemouth.
Harry Winks (groin) has also returned to training, while Victor Wanyama (thigh) and Jan Vertonghen (ankle) are being assessed after sustaining injuries against Ajax.
Danny Rose, who was replaced by Ben Davies late on in Amsterdam, is also a doubt with a hamstring problem.
Spurs can guarantee their place in the Champions League by earning at least a point against Marco Silva's side, with Arsenal only capable of jumping ahead of them into fourth if they win, Spurs lose and there's an eight-goal swing in the Gunners' favour.