The duo, whose new film Drive screened at the Cannes Film Festival and opens in cinemas this September, will remake the cult '70s science fiction film with producer Joel Silver and Warner Bros.
"Joel said the other night, 'Take your time and make it good. It doesn't have to be ready at any point'," Gosling told the Los Angeles Times.
The 1976 Logan's Run took place in a utopian world where life must end at 30. Michael York starred as Logan, a "Sandman" who tracks down those who try to escape death. It is based on William F. Nolan's novel, in which the age of termination is 21.
Refn noted that the original movie is "dated in the sense that everything came true".
"They've been trying to make it for years with the notion of just trying to remake the original movie," he said. "And it has to be rethought."
Bryan Singer and Tron: Legacy director Joseph Kosinski have previously tried to mount remakes of Logan's Run.
"We'll put together a team of futurists and artists and we'll dream on this world," Gosling said.
> Ryan Gosling's Drive: In Pictures
Watch Ryan Gosling in an extended Drive clip below: