Bloomberg News reported the merger talk, citing Swiss economic magazine Bilanz.
The cookie maker pared its gains and was up less than 6 percent after Reuters reported, citing sources, that Mondelez has not heard from Kraft-Heinz. Mondelez told CNBC that it does not comment on market rumors or speculations.
Mondelez separated from Kraft in 2012 and has focused on widening its profit margins by reducing costs through divestitures and asset sales. It is currently in the middle of a $3 billion cost saving program, which runs through 2018.
In June, the Hershey board unanimously rejected an offer from Mondelez to acquire the company. At the time, observers speculated Mondelez was seeking the merger in order to remain an independent company and not become a target for acquisition itself. Mondelez had been under pressure from activist investor William Ackman to either grow revenue faster or sell itself to a rival.
Kraft-Heinz declined to comment to CNBC.
Kraft-Heinz shares gained about 3 percent in extended trade, following the news. Mondelez shares are down a little more than 4 percent year to date, but up slightly more than 3 percent in the past month.
—Reuters and CNBC's Christina Cheddar Berk contributed to this report.