Shake Shack (SHAK - Get Report) won't be going beyond offering traditional meat hamburgers anytime soon, ruling out the possibility of following in the footsteps of McDonald's (MCD - Get Report) , Restaurant Brands International's (QSR - Get Report) , Burger King and A&W, who have all introduced plant-based protein, meat-less burgers, the company's CEO said on Friday.

"We have no intention of doing it today," Shake Shack CEO Randy Garutti told CNBC's "Squawk Box " on Friday. "We want to watch and see how this plays out."

Garutti said that he was "fascinated" by the early sales numbers released by restaurants that have already introduced Beyond Meat (BYND) meat-less patties, but that he wants to see if those numbers continue.

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"Shake Shack was built on doing classic things better than other people did them, so let's watch a little bit," Garutti said.

Shares of Del Taco Restaurants (TACO - Get Report)  gained some positive attention this week following that company's announcement it will be adding two new burritos to its menu that use a new meatless faux-beef product being introduced by Beyond Meat.

Canada's Tim Horton's, another subsidiary of Restaurant Brands International, also recently announced that it is now offering faux-meat breakfast sandwiches made with Beyond Meat products at almost 4,000 of its locations. 

Shares of Beyond Meat were down 7.24% at $153.21 in trading Friday on the Nasdaq Stock Market. Shake Shack shares were down 0.25% at $67.15 on the New York Stock Exchange.