Hingis announced last week she would dissolve her highly successful partnership with Kournikova to link up with Monica Seles.
Keen to play down talk of a rift, Kournikova said: "A lot of players change partners all the time. This is our sport and that's just the way it is."
The so-called "Spice Girls" had won nine titles together since teaming up two years ago with their biggest victory coming at the 1999 Australian Open.
Media reports claimed the bust-up was a result of an on-court row they had during an exhibition tournament in Chile in November.
But Kournikova, speaking to reporters after her match against Elena Bovina at the Sydney International on Friday, insisted their public spat had nothing to do with the split.
"It's not like a break-up, it's just that we've both got different partners," the 19-year-old Russian said.
"It's not like we're never going to see each other or talk to each other."
Kournikova said the split had been amicable because she had also wanted to cut down on her doubles commitments to concentrate on singles.
Despite raking in millions in endorsements and finishing last year ranked eighth in the world, Kournikova is still chasing her first singles title as a professional.
She was beaten by Australian teenager Jelena Dokic last weekend in the final of an exhibition event in Hong Kong and admitted she was becoming frustrated by her long run of failures.
"I know I'm working hard but you never know when it's going to happen," she said.
Kournikova's chances of winning her first title could well depend on how she goes against the Swiss Miss with the pair scheduled to meet in the semifinals of the Sydney event.
Hingis, as top seed, was given a bye in the first-round while Kournikova looked impressive as she swept past her fellow Russian Bovina 6-4 6-4.
"I knew what I had to do, I had my game plan and I think I played very good," she said.