AmazonFresh has been expanding slowly in the U.S., but the grocery delivery service could be making the jump across the pond soon. A new report from British newspaper The Times claims Amazon is expanding the Prime perk overseas in the near future.

If the rumors are true, Amazon may still face an uphill battle. The company faces competition from British online supermarket Ocada and others. The Seattle-based retail giant's prices may also be a turnoff for some.

To use AmazonFresh, you need to sign up for a special $300 per year membership, which comes with Prime benefits built in. On top of that, you'll be paying for delivery on orders under $35 along with tips for the driver.

Of course, Amazon doesn't need the service to be an immediate hit. The company already rakes in plenty of cash through traditional online sales. AmazonFresh still feels like a pet project, even if it's starting to pick up speed.