NEW YORK (The Street) -- For Coca-Cola(KO) - Get Report , the time may be finally ripe to embrace selling more than sugary soda and other beverages. 

According to a report from Reuters, PepsiCo(PEP) - Get Report and Coca-Cola are competing to potentially invest in Greek yogurt maker Chobani. A deal could value Chobani at as much as $3 billion. Chobani is looking for a strategic investor to help expand its supply chain, distribution, manufacturing base and geographic footprint for its newer yogurts such as Flip, which comes in a container with crunchy toppings.  

A Coca-Cola spokesman declined to comment specifically on the Chobani rumors. 

Chobani boasts more than one-third of the U.S. market share for Greek yogurt, according to data tracking firm Nielsen. So far this year, Chobani has added products such as "Peanut Butter Dream," its take on a Reese's peanut butter cup, and "Strawberry Summer Crisp," a flavor that resembles a bite into a strawberry shortcake.  The company has added oats to its yogurt in a bid to appeal to fans of cold cereal and oatmeal.

Chobani has even gone so far as target the boring baby food aisle dominated by Gerber, a subsidiary of Nestle. It recently released its all-natural "tots" line, with two flavors -- mango spinach and banana pumpkin -- that are packaged in squeeze packs.

Coca-Cola has a track record of making minority investments in emerging consumer companies, taking stakes in single-serve coffee maker Keurig Green Mountain (GMCR)  and energy drink purveyor Monster Beverage(MNST) - Get Report .

The problem is that those stakes, and a relentless focus on selling carbonated beverages, have left Coke underrepresented in the expanding environment for healthier snack and breakfast foods. Meanwhile, Coke's arch rival PepsiCo has long held a 50% stake in hummus maker Sabra, which has given the company exposure to consumers seeking healthier fare.

PepsiCo has also begun to better leverage its Quaker Oats business into instant oatmeal with dried fruits, 3-minute steel cut oats and snack bars, further helping it to diversify away from carbonated soft drinks.

But Coke remains largely at the mercy of a pressured carbonated soft drink market. Total U.S. carbonated soft-drink sales volume fell 3% last year to 8.9 billion cases, the ninth straight year of decline and the smallest number of cases sold since 1995, according to Beverage Digest.

Things have not gotten much better thus far in 2015, with diet cola sales especially stuck on a downtrend. Coke noted its Diet Coke brand continued to struggle in the U.S. during the second quarter. Global volume for Diet Coke fell 7%, according to the company.

According to data from Beverage Digest, Diet Coke's U.S. volume fell 5.2% in the second quarter. Coke's challenged results in diet colas mirrored those of PepsiCo, with Beverage Digest estimating that Diet Pepsi's volume fell 8.5% in the second quarter.

Not everyone thinks that Coke is even that interested in Chobani, however.

"While Coca-Cola has certainly moved more into value-added dairy with investments in products like Fairlife enhanced milk, taking a stake in a yogurt company as a food play would certainly be a departure from its laser-like focus on beverages," said Duane Stanford, the editor of Beverage Digest.