Murphy, 52, made a name for himself in the first movie as the hard-talking, smartest cop on the block, before building upon that success with the second film, which was helmed by the late director Tony Scott.
The new script is currently being penned by the "Mission Impossible: Ghost Protocol" masterminds Josh Applebaum and Andre Nemec.
The film company's interest in reviving the franchise is believed to have been sparked by the pilot episode for a spin-off TV series, which featured Brandon T Jackson as Foley's son.
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