According to the Los Angeles Times, Linklater has already met with executives at Warner Bros several times to discuss his vision for the film, in which an ordinary man is transformed into a fish.
Although a deal is yet to be signed, executives are said to be impressed with Linklater's recent work on hybrid animation films like A Scanner Darkly and Waking Life, which follow a similar art direction to what they envisage for the Mr Limpet remake.
If a deal is struck, the project will reportedly move away from the original film's links to World War II and the Nazis, and focus instead on a more modern setting.
Last year, it was claimed that The Hangover star Zach Galifianakis was in talks to play the lead role in the film, although no further mention of the actor's involvement has been reported since.
The project has been gestating in Hollywood for a number of years, with Enchanted director Kevin Lima originally attached to the film in 2009.
Warner Bros has yet to officially announce a director for The Incredible Mr Limpet.
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