Hyundai wants to focus more on SUVs and is reportedly considering developing a larger crossover based on the Genesis luxury sedan.

The news was broken by Reuters, which cited four people familiar with the matter. However, one of the people said there is no certainty Hyundai will launch the new vehicle, due to concerns about the company’s lack of brand power in the premium SUV segment and fears that oil prices may go up again.

Still, if Hyundai gives the green light to the project, the large SUV is not likely to arrive earlier than two or three years from now.

“We are timid when it comes to bigger SUVs,” said an unnamed source familiar with Hyundai’s vehicle development. The automaker is said to consider an internal proposal made last year to develop Genesis-based SUVs, said a second source. The aim would be to use the appeal of the Genesis to help grow Hyundai’s overall brand image.

US sales of the Hyundai Genesis rose by more than a third between January and May to approximately 15,000 units, far exceeding Hyundai’s overall sales gains of just 2 percent.

At the end of July, Hyundai will stop making the Veracruz, its biggest SUV, according to the company’s South Korean labor union. However, the automaker said this doesn’t mean it’s giving up on a large SUV lineup.

“We are considering developing premium, large SUVs based on customers’ needs. We plan to respond to the fast-changing market centered around SUVs by beefing up our SUV line-up,” Hyundai told Reuters in an email.

Hyundai currently offers only two SUVs in the US: the compact Tucson and the mid-sized Santa Fe (pictured).

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