The studio’s film group president is leaving the role after six years.
Studio chairman and CEO Brad Grey and vice-chairman Rob Moore are understood to have been concerned about the studio’s slight slate.
Paramount’s next home-grown release is Terminator: Genisys on July 1.
They have offered Goodman a producing deal and expect to find a successor within 60 days.
Goodman arrived in 2008 from DreamWorks and played an integral role in the Transformers, Mission: Impossible and Star Trek series.
The studio also released the global hit World War Z on his watch, although the film was delayed and reconfigured due to budget issues.