Adidas partners with Amazon to sell its products online in the United States.

It's looking at possibly expanding the relationship, according to Adidas CEO Kasper Rorsted.

Rorsted said in an interview with Business Insider that he isn't too concerned about Amazon's private-label growth, but he is more worried about the potential for price erosion and losing the direct connection to the customer.

Adidas sells on Amazon in the United States — and only in the United States.

The global sportswear retailer operates a store at Amazon.com/Adidas. Despite the fact that by most analysts' estimates, Amazon has just about half of all online sales, Adidas doesn't consider it its most important outlet for selling online.

"Our e-commerce strategy is all about us connecting directly to the consumer," Adidas CEO Kasper Rorsted told Business Insider in a recent interview. "That's the most important part."

Instead, Rorsted says that Adidas.com is its most important store in the world.

Still, Amazon's dominance in the US e-commerce market makes it hard to ignore. Rorsted said that Adidas currently has a "good partnership" with Amazon and is looking at whether it should expand it.

But, he has a few concerns.

"We positioned the brand [in the] right way [so] that it doesn't become a value-driven purchasing experience," Rorsted said. "Of course, that is a challenge to our relationship with Amazon because Amazon is driven by two parameters, which are efficiency and price."

Amazon isn't a traditional sporting goods retailer, and the reach its prices have is immediately obvious. Its drive to provide the lowest cost could potentially damage Adidas' ability to sell at full price, Rorsted said.

"We're working intensely with Amazon to ensure that we have a good partnership, which we have today, but we don't jeopardize the brand based on the drive for the lowest cost," he said.

Another issue is data sharing, which Rorsted said Amazon does to a lesser degree than Adidas' other online partners.

"For us, getting access to the data is fundamental. Not only in the context of being able to engage directly with the consumer from a commercial standpoint, but getting the appropriate feedback for the creation of the next generation of products," he said.

"That, of course, we're working on," Rorsted added. "It's a battle we have with Amazon."

Still Rorsted, doesn't worry about Amazon creating its own private-label sports brands using data from selling Adidas products.

"We create the right products that are cool, that are innovative, we have the right materials, the right manufacturing — that competition is not the concern we have," Rorsted said. "Whether Amazon would want to come up with a shoe: I think eventually that will come or it is coming. That's not the concern of ours."

The concern instead is that "we don't tarnish the brand and we don't make price the most important parameter in how the product is being sold," Rorsted said.

"The moment you do that, you don't have a brand anymore."