A source at ESPN, whose name was not reported, told Sports Illustrated the network had made an "aggressive offer" to keep Andrews, 34, before her contract expires at the end of June.
Andrews' agent declined to comment on her plans now that she has left the network, but it appears she might join Fox Sports, The Hollywood Reporter said Friday.
Sources with knowledge of Fox's plans said it's almost certain Andrews will take a role at the network, THR said.
Andrews most recently has hosted the ESPN College Gameday preshow. In her eight years at the network, she has covered Major League Baseball, the College World Series, and college basketball and football.
In 2008, she was at the center of a stalking case in which a man watched her through peepholes at her hotel rooms in Nashville and Milwaukee. The man was sentenced to 30 months in prison and is scheduled to be released next month, THR said.