Belgium international Vertonghen has been sidelined since picking up an ankle injury in Spurs remarkable comeback win against Ajax, and was seen leaving the Amsterdam Arena with his foot in a protective boot.
Kane, meanwhile, has missed Spurs nine games since sustaining significant lateral ligament damage to his left ankle against Manchester City, and Spurs initially thought he would be out until the end of June.
According to The Guardian, both players have recovered quicker than expected - with Vertonghen already out of his protective boot and Kane seen running across the pitch to celebrate with his team-mates after the win against Ajax.
Manager Mauricio Pochettino has acknowledged that Vertonghen has time on his side, but he wont be rushed back if hes not fit and able to play.
"Theres a lot of time for him to come back, I hope to have all the squad available but if someone is not available then its about the team," Pochettino said. "We are going to assess each individual and give more individual work than collective."
When Kane sustained his injury, Pochettino told the clubs official website that he was "sad" for the 25-year-old, offering a fairly blunt assessment of his chances of returning this season.
"He’s okay, he’s always a positive guy but of course it’s so disappointing. It was a tough moment for him, for us and it’s about wishing and to hope that it’s not a big issue but it’s true that the news is not good.
“We’ll see. Day-by-day we’re assessing him and trying to help him to recover as soon as possible."
He appears to have made significant progress in his recovery, though, and could now feature in European footballs showpiece event - and his return would be a huge boost for Spurs.
Kane has scored five goals in eight Champions League games, with Lucas Moura stepping up in his absence against Ajax with a wonderful second leg hat-trick.