The film, inspired by the oil rig explosion in the Gulf of Mexico that took place on April 20, 2010, honors the brave men and women whose heroism saved many on board during the world's largest man-made disaster.
"Is it special to work with your family? Yeah, it is," Russell told ET. "And I'm looking forward to that in the future."
Russell helped raise Kate and her brother Oliver after their biological father, Bill Hudson, split from their mom Goldie Hawn in 1982. Russell and Hawn have been partners since 1983.
"I look forward to really working more with him," Hudson said.
The two could get another shot at sharing the screen together soon if all goes according to plan.
"Kate and I are involved in a project," Russell said. "The fact that it's family, maybe Goldie [Hawn] would play a part in it at some point. Hopefully, I'll be talking to you in a couple of years about it."
Deepwater Horizon, also starring Mark Wahlberg, John Malkovich and Gina Rodriguez, hits theaters Sept. 30.