Snoop Dogg lives large, but big enough to turn a whole nation into his crib?

A British tab said the famed rap star was in talks to rent the nation of Liechtenstein — the whole country — for a video shoot, in a proposed deal that fell apart only due to Dogg’s time constraints.

But The Daily Mirror’s report was news to authorities in the tiny, affluent principality today. They scoffed at the notion that their country was looking to roll with Dogg.

“There is no ‘For Rent’ sign on our country,” ambassador Claudia Fritsche told The Post. “No part of any government agency is involved in this.”

Despite Fritsche’s harsh words, Liechtenstein’s ambassador to the United States was laughing more than scowling about the concept of Dogg renting the Staten Island-sized European nation.

A Liechtenstein property manager, Karl Schwaerzler, insisted to the Mirror that Dogg indeed wanted to rent all 61 square miles of Liechtenstein for a video shoot.

“We’ve had requests for places and villages but never one to hire the whole country before,” he said. “It would have been possible, but Snoop Dogg’s management did not give us enough time.”

Reps for Snoop Dogg could not be reached for comment today.

Liechtenstein officials theorized something was lost in translation between Dogg and Schwaerzler’s camps.

Schwaerzler’s business specializes in brokering deals between European villages and corporations to stage large-scale events where companies ceremonially rent the entire community.