Spain's Deoleo, the world's largest olive oil producer, says U.S. President Donald Trump's threat to impose 30% tariffs on imports from the European Union could translate into higher prices for U.S. consumers — as well as limited access to a superfood staple.

Trump has threatened to raise tariffs on the 27-member bloc from Aug. 1, in what would mark a steep jump from the current 10% duty.

The EU has long been scrambling to reach a trade deal with the U.S. and is considering its options ahead of Trump's deadline, including the prospect of countermeasures.

Huge uncertainty persists over whether the U.S. and EU can strike a deal over the coming days, although a blockbuster framework agreement between the U.S. and Japan has raised hopes of a breakthrough.

Deoleo, the maker of household olive oil brands such as Bertolli and Carbonell, told CNBC that the Trump administration's trade measures could have an impact on American consumers, particularly given limited U.S. production.

"It is worth noting that approximately 95% of the olive oil consumed in the U.S. is imported, so such policies will affect end users," Deoleo CEO Cristóbal Valdés told CNBC by email.

The Spanish company said the U.S. accounts for more than a quarter of its total revenue, making it a strategically important market.

Around 40,000 acres (16,187 hectares) of olives are planted exclusively in the U.S. for olive oil production, according to the American Olive Oil Producers Association.

By comparison, the EU is known to be the leading producer, consumer and exporter of olive oil, with roughly 4 million hectares (9.88 million acres) dedicated to the cultivation of olive trees across the region.

Most of the world's supply of olive oil comes from the Mediterranean, with southern European countries such as Spain, Italy and Greece among the world's leading producers of the precious commodity.

Spain, in particular, is the biggest olive oil producer in the EU and a global reference for prices.

As part of its preparation for a higher tariffs rate, Deoleo's Valdés said the company intends to ramp up its communication, marketing and consumer engagement efforts to ensure olive oil remains an everyday staple.

"Beyond institutional dialogue, we are strengthening our value proposition in the U.S. through consumer awareness campaigns about the benefits of olive oil and a renewed commitment to our brands—especially Bertolli, which today represents trust and consistency for American consumers," Valdés said.

Deoleo's chief executive also said the olive oil producer would continue to keep all strategic options open, while working on logistics and supply chain improvements to respond to different market scenarios.

"However, beyond tactical decisions, our main priority is to protect American consumers' access to a food product that is essential to their health. Access to olive oil should not be penalized — it should be promoted," Valdés said.

As U.S. tariffs on EU goods first came into effect in early April, analysts at commodity data firm Expana warned that a reduction in U.S. olive oil imports could have "serious repercussions" for the global market.

They cited market players as saying that such a shift could create a supply glut in the EU, leading to further downward price pressure and intensifying competition among producers.

It's not just olive oil exporters that have been rattled by Trump's latest tariff threats, however. Irish whiskey firms, Italian cheesemakers and French wine producers are among those who have sounded the alarm over the potential impact.