Europe's supply of the Xbox One S 2TB model is somewhere between dwindling and non-existent, according to Eurogamer.

The site also reports that Microsoft has no plans to replenish stock of the white console, which launched worldwide last week.

"We're excited by the reaction from fans for the Xbox One S," a Microsoft spokesperson told Eurogamer. "While stock of the 2TB has sold out, gamers can pre-order the Xbox One S 2TB Gears of War Limited Edition console.

"We will be sharing further details on other Xbox One S bundles and variations in the coming weeks."

It looks like the shortage is yet to hit New Zealand, with Mighty Ape still reporting the 2TB console model as "in stock".

Additional models are also on the way, with smaller 1TB and 500GB white models releasing August 23.

The Gears of War 4 Xbox One S bundle is set to release on October 7, and will feature a 2TB hard drive.