Villas-Boas, who managed Spurs between 2012 and 2013 when Kane made his Premier League bow, said on Tuesday if the striker wanted to win trophies and honours, he would have to leave White Hart Lane.
Kane hit his 150th club goal at the weekend to earn Tottenham a 1-0 win at Crystal Palace which left them in fourth place in the Premier League table.
Former Real Madrid president Ramon Calderon has signalled that Kane would be one of his club’s major transfer options this summer, ahead of Bayern Munich forward Robert Lewandowski.
But on Tuesday Tottenham manager Pochettino, preparing his side for Wednesday’s fifth-round FA Cup replay against League One strugglers Rochdale at Wembley, swept aside all the rumours, saying: “I have no reaction to that.
“We are all here to help the club achieve and win titles. Harry is very happy here. Of course he wants to win titles with us. All of us do.”
Pochettino, who will again be without defenders Toby Alderweireld and Jan Vertonghen on Wednesday, added: “We are very happy with our squad.
“There are always a lot of rumours, about our players and about the manager. I think I heard we even had an offer for the chairman! There are always rumours.”
Pochettino, whose team will face an away quarter-final to Swansea if they can overcome Rochdale, has denied that playing home games at Wembley will give his team an advantage if they make it through to the semi-finals.
Some teams have privately expressed disquiet that playing at Wembley all season would give Spurs an advantage should they reach the last four, when both ties will be staged at the national stadium.
But the Argentine laughed off the suggestion, pointing at the difficulties Spurs had in early games this season at the stadium.
“Now it’s an advantage? Before, people were saying it was a disadvantage. Remember the Wembley hoodoo?
“At the time people wanted me to say yes, it is a problem playing at Wembley, and to recognise the problem. I laugh – but it’s not an advantage.
“We are playing at a stadium that is massive motivation for our opponent to play at, for them to have the opportunity to play there.”
Spurs drew 2-2 at Spotland in the first game between the clubs two weeks ago with a patchy display.
But Pochettino insisted: “We were not complacent up there. These are all difficult games – look at Manchester City, they lost at Wigan.
“I do not want to look too far ahead. We need to win, and it will not be easy. This is a very important game.”