It was originally thought that the striker would be absent for up to 6 weeks, ruling him out for the majority of the rest of the season.
"Harry's had a few sessions before, and today he was involved with the team," Pochettino said.
"And we'll see tomorrow whether he will start the game or be on the bench. But it's good news that he's ready. He feels good about his recovery.
"It's very good news for him and for us. He's an important player for us, and for him to be available for us is great.
Kane's rapid recovery would also see him return in time for two vital London derbies, to the delight of his manager, who has described his striker as a "special player".
Spurs play Chelsea in the FA Cup semi-finals on April 15, before playing Arsenal in the last ever north London derby at White Hart Lane on April 30, a match which could have serious ramifications for who finishes in the top four.
"We are happy, he's ready, maybe normally after one month out you need to feel the competition," Pochettino added. "But he's a special player, he tries to push himself a lot.
"We do need to decide tomorrow if he will be in the starting XI or on the bench. But the good news is he's back. And he's our main striker.
"What Harry means for the team is a massive boost for us and it's fantastic news.
"He's always desperate to play, he's always pushing you to try to let him train, play, and score goals. His character is unbelievable."
Tottenham have meanwhile announced that Danny Rose – also absent with ligament damage – is on track for a return by the end of the month and could play against Arsenal.
The full-back was injured in a goalless draw against Sunderland at the end of January.
Pochettino does however have a minor injury crisis at the back.
It means the manager could hand a first-team debut to Pau Lopez, a 22-year-old who has been restricted to appearances for Tottenham’s U23 team since joining from Espanyol on loan at the start of the season.