"We are aware that Trian has disclosed taking a significant stake in Sysco. We are aware of their actions," a Sysco spokesman told CNBC.
Trian sees an opportunity to improve Sysco's margins and to return more capital to shareholders, sources said. Peltz has a significant experience in the food industry, with positions over the years in Kraft, Mondelez, Wendy's, Pepsi and others—so this is right in his wheelhouse.
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Given Sysco's performance over the past five years, it's easy to see why Trian would perhaps see an opportunity: Shares have significantly underperformed the market, total shareholder return is less than half of the S&P over that period, and earnings-per-share are down.
"Sysco welcomes collaborative discussions with investors who share our interest in creating value by marketing and delivering great products to our customers with exceptional service," the company said in a statement, adding that it has recently "engaged with Trian and expect to continue a constructive dialogue."
There was also a failed merger with US Foods—blocked by regulators and terminated this past June—that cost shareholders. Sysco paid a break-up fee of $300 million to US Foods and another $12.5 million to the Performance Food Group. At the time, Sysco also announced a $3 billion share buyback.
Since Sysco's fiscal calendar means the board nomination window will close next Friday, there could be three potential outcomes between now and then.
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Firstly, there could be an agreement between the two sides over the next week. The company could extend the window to continue negotiating. Finally, there's even the possibility of a proxy fight, which sources said is not being ruled out—although Trian is said to hope that one won't be needed.
It's been a busy year for Peltz: A proxy fight with DuPont, and Trian recently announced another new position in Pentair.
—CNBC's Everett Rosenfeld contributed to this report.