Slot is under consideration for the Spurs job but Te Kloese insists Dutch champions Feyenoord have not received an approach for their coach.
Luis Enrique is also in the frame to become the next Tottenham manager but Spurs have doubled down on their stance that Julian Nagelsmann is not in the frame.
Slot did not rule out a move to Tottenham on Friday but Feyenoord want to offer him a new contract after he guided them to the Eredivisie title.
Speaking to ESPN, Te Kloese said: "[Slot] still has a contract for two years. That has been said before and we have not been approached by any club.
"It is up to Arne to say something about that [his future]. But for us there is no ambiguity about it. We assume that he will remain the trainer of Feyenoord.
"He has a contract for two more years and this summer there is no release-clause in his contract, so we can say no if we want. And we have quite a good story here as well.
“Champions League next year, a lot of new players were signed last summer and they proved real good players in this team and their contracts also run for quite some years to come. So we have something here to look forward to."
Te Kloese also claimed he has turned down an approach from Spurs to become their new sporting director.
He said: "It’s not an option right now," Te Kloese said. "I said ‘no’ and I also don’t have any interest. I’ve made the choice to work for Feyenoord and that is still a great honour.
“We have made really good steps last year and then to say: ‘Let’s hear what I can do for other clubs,’ is not an option for me. I want to be very clear: It will not happen."