While a guest on the Empire Spoiler Podcast with executive producer Simon Kinberg, director Bryan Singer revealed that he has a small cameo in the film. His cameo is brief, as he's dispatched pretty quickly by Wolverine/Weapon X. Singer begins discussing the scene and getting Jackman aboard at the 24:00 minute mark. Below, we've included a quick transcription for those of you on mobile or tablet devices.
"I have a little cameo, I'm the guy with the machine gun..screaming. When I look at it, I couldn't recognize myself so I knew no one else could. But it was cool to get killed by Wolverine. It's now one of the many things I can put on my resume. When went back later to film the Wolverine segment because Hugh was training for the next Wolverine sequel and we wanted him in a certain kind of shape. At first, Hugh was reticent to do it, but once I explained it to him, what the scene is and why it's there, he agreed to do it over the phone, which is unusual. Usually there's a bit of negotiation involved, but he said 'You can call my Agent, but I'm in, I love it.'"