Spurs opened talks with Kane earlier this year over an extension to his current deal, which runs until 2020 and is understood to be worth around £50,000 a week.
A resolution, however, is yet to be found, with Tottenham determined not to dismantle their strict wage structure.
Hugo Lloris remains the club's highest earner on around £80,000 a week and the goalkeeper is also yet to extend his deal at White Hart Lane, which expires in 2019.
"For us they are players that are very important, Harry and Hugo," Pochettino said.
"They are very happy to be here and we are very happy that they are here.
"Maybe there are a lot of rumours that can affect our fans but the fans need to be quiet and have no worries about this because the players show their commitment to the club, they want to be here for the long term.
"I think the club and the players are talking about maybe improving or having extended contracts
In the future I think it's not a big problem to do."
Kane's commitment is particularly important given his unparalleled status among Tottenham's fans, as well as his outstanding contribution on the pitch.
The 23-year-old has been the club's top goalscorer for the last two seasons and he won the Premier League's Golden Boot award in May.
His success, however, has reportedly prompted Kane to request parity with this country's other top strikers, like Leicester's Jamie Vardy and Liverpool's Daniel Sturridge.
Pochettino believes such comparisons are unhelpful.
"You cannot compare their situation with another player," Pochettino said.
"In my life, when I was a player and now as a manager, I need to be happy with what I won, what I need, but never to compare with another, because it's not important.
"I don't know, what happens in another club is their business
I can say that they're happy
I can feel every day that they're happy
I'm calm.
"I 100 per cent trust the club and (chairman) Daniel Levy
He's doing a fantastic job with the club
The future is brilliant.
"All the players want to commit to the club and you have plenty of examples in the past few months."
After being released from England duty, Kane has undergone intensive training since Monday as he continues to seek sharpness following his seven-week lay-off with an ankle injury.
He is expected to start against West Ham on Saturday but with crunch games against Monaco in the Champions League and Chelsea to come, Pochettino must manage a number of fitness concerns in his squad.
Toby Alderweireld has not recovered from a leg injury, which has taken longer to heal than expected, while Erik Lamela and Ben Davies are out with hip and ankle problems respectively.
Dele Alli is close to overcoming a knock to his knee and will be available against Monaco on Tuesday, even if Saturday comes too soon for the midfielder.
Christian Eriksen and Danny Rose are likely to shake off hip and foot injuries sustained over the international break.
Alderweireld's prolonged absence is a concern for Pochettino, who had initially hoped the Belgian would be available to face Leicester almost three weeks ago.
"From the beginning we believed it would be a very short process to be available again," Pochettino said.
"But in the end the recovery was very slow
The knock he got affected the nerve and the process to recovery was very slow.
"Today he is near to start training with the group
That is very good news
Maybe one week to 10 days more to be available if all goes well."
Source : PA
Source: PA