Richardson says he had a "very productive meeting" with Chavez on the issue Saturday night.
The Democratic governor is in Venezuela not as an official envoy but at the request of the hostages' families. The former U.S. presidential candidate and energy secretary has experience as a troubleshooter in other countries.
The Revolutionary Armed Forces of Columbia captured the three American defense contractors when their plane crashed in the Colombian jungle in February 2003. Richardson also has expressed concern for other hostages including French-Colombian captive Ingrid Betancourt.