It's time to put a veil over that red, pigtailed wig.

Wendy's (NYSE:WEN) has been teasing investors for several months with the potential of being acquired, and now the most eligible bachelor is taking a closer look.

Billionaire investor Nelson Peltz, who has been vocal about the untapped potential of the country's third-largest burger chain, has entered into a confidentiality agreement with Wendy's. Peltz is eyeing the purchase for either his Trian private equity fund or as a combination with his stake in Arby's parent company, Triarc (NYSE:TRY). Either way, this should be Wendy's best shot at being acquired at a healthy premium.

Wendy's is fresh out of external catalysts. It sold off its Cafe Express and Baja Fresh concepts and spun off Tim Hortons (NYSE:THI) last year. However, the push for a sale is still surprising, given Wendy's recent momentum in making its mark in the breakfast business.

Wendy's lacks the breakfast-menu presence of burger-flipping rivals McDonald's (NYSE:MCD) and Burger King (NYSE:BKC), but it's out to change that. Last week, Wendy's announced that it now has 500 locations opening up for breakfast. And though that's still less than 10% of the chain's 6,300 units, breakfast may be a savior for the company. Early-morning grub was one of the reasons behind Burger King's strong showing last week. Patrons may spend less for that first meal of the day, and staffing a restaurant doesn't get any cheaper, but offering breakfast is ultimately incremental when done right.

One can argue that Wendy's should see whether it fails at winning over a breakfast crowd before running off to get hitched. However, the initial success is the reason Peltz -- or any other potential suitor -- may be attracted to Wendy's right now.

We'll see how it goes. For now, with Peltz digging deep into the financials and making no bones about his desire to pay a premium for the chain, it would be surprising to see him walk away without donning that crazy red wig.

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Longtime Fool contributor Rick Munarriz enjoys the new chunky chicken salad sandwich at Wendy's, but he won't be making a buyout bid. He does not own shares in any of the companies in this story. He is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early. The Fool has a disclosure policy.