Eric Stonestreet Is Not Dating Charlize Theron

Eric Stonestreet and Charlize Theron in April

Dimitrios Kambouris/WireImage

updated 08/25/2015 AT 8:16 PM ET

originally published 09/24/2012 AT 4:00 PM ET

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On Sunday night, Eric Stonestreet took home an Emmy, but the Modern Family star did not have Charlize Theron on his arm at L.A.’s Nokia Theatre, contrary to tabloid reports.

Shooting down rumors of a romance, Stonestreet took to Twitter true to his comedic roots. “I wish people would stop spreading rumors that Charlize Theron and I are dating,” he wrote. “Its starting to make Halle Berry jealous.”

He also joked about it on the Emmy red carpet, deadpanning to PEOPLE: “Charlize is a beautiful woman and I just wish she’d stop calling.”

Suddenly, he looked around and said, “Oh, who’s that looking at me now? Is that Mila Kunis? Hi, Mila.”

Stonestreet, who won a trophy in a race featuring costars Ty Burrell, Jesse Tyler Ferguson and Ed O’Neill for outstanding supporting actor in a comedy series, has a not-so-steamy (but still special) Emmy date to root him on: his best friend Paul.

“He dared me to audition for the first play I ever did at [Kansas State University],” Stonestreet said.

• With reporting by JULIE JORDAN and JENNIFER GARCIA