Domino's CEO needs a new gig. Chipotle is hiring.

New Ford CEO excited for driverless Domino's
New Ford CEO excited for driverless Domino's

Domino's turnaround wizard is looking for his next gig. Chipotle's desperate for a leader to help it get back on track.

Wall Street is buzzing about Patrick Doyle's departure from Domino's and already speculating whether he'll head to Chipotle after he steps away from the pizza chain in June.

Doyle threw cold water on the idea to the Wall Street Journal. But his history at Domino's would make him the perfect fit for Chipotle's vacant CEO slot. (Chipotle declined to comment for this story.)

Chipotle announced in November that founder and CEO Steve Ells would give up his CEO title, the latest twist for a company that has struggled to win back customers after a 2015 E.coli outbreak rocked the chain. Investors are still queasy about Chipotle's (CMG)stock too. Shares have fallen more than 50% over the past three years.

Related: Chipotle looking to hire a new CEO

Although Chipotle's woes began with the food safety scare, its failures extend to understanding customers' habits and marketing to them effectively, said BTIG analyst Peter Saleh.

Chipotle has also fallen behind competitors on digital innovation and mobile ordering -- areas Doyle could immediately address.

"He fits the bill well," said Morningstar analyst R.J. Hottovy, who emphasized Doyle's experience repairing a damaged brand.

Doyle, 54, was a superstar at Domino's. When he took the helm in 2010, the company was in the dumps.

Sales were flat and critics were comparing the pizza to cardboard crust. Domino's was trading at under $10 a share.

Doyle took on the company's battered image head first.

He filmed commercials reading customer complaints and admitted the pizza was lousy. Domino's would upgrade its ingredients and roll out a better pie, Doyle vowed.

"There comes a time when you know you've got to make a change," Doyle said in an early ad. He's done exactly that.

Domino's has muscled out larger rivals Pizza Hut and Papa John's during Doyle's run, delivering an impressive six straight years of sales growth. Its slice of the pizza market has grown to 15% -- the largest in the world -- as it nears 15,000 stores. Domino's (DPZ) stock is trading at more than $200 a share.

Related: Domino's testing self-driving pizza delivery

The company has excelled online and through its mobile app. Customers can now order Domino's with emojis on Twitter and Facebook Messenger and from Amazon Echo and Google Home.

Digital traffic accounts for 60% of sales, the company told investors Tuesday.

--CNNMoney's Paul R. La Monica contributed to this story.

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