The 'Rope' rockers, who recently topped the UK and US album charts with their new record Wasting Light, said that they will play the event if their performances at festivals this summer go well.
"We may play Reading in the summer next year, if we get through all of this run okay," Hawkins told the Daily Star. "Festivals are where we cut our teeth and became a good band."
The Foos have been confirmed to perform headline slots at this year's Radio 1 Big Weekend, T in the Park and Isle of Wight festivals, with Hawkins explaining that the band enjoy the festival atmosphere despite the chaotic setup.
"The sound is crazy because there's no soundcheck. We have the best crew in the world, but all they can do is try to make it as comfortable as they can for you.
"You get up there and just have to do it."
My Chemical Romance, Pulp, The Strokes and Muse are to headline this year's Reading and Leeds Festivals.
Watch the video for the Foo Fighters' latest single 'Rope' below: