The Tennessean reports Kalodimos said in a statement the end came "with a letter left on a desk, no conversation, no face to face meeting, no thanks."
Her latest contract expired Dec. 31. The station is owned by the Meredith Corp.
The veteran anchor also said there was no real offer to extend her contract as WSMV asserted, just an offer for two more weeks "so that the station could create the illusion that I retired."
Kalodimos' statement came just a few hours after WSMV sent a release to the Tennessean saying Kalodimos gave "no timely responses" to the station's offer of "an extension of her contract for the purpose of discussions."
The station, in its statement, said it would not be "appropriate to comment further on personnel matters."
The split comes about five weeks after Kalodimos was named as a witness in an age discrimination suit filed by three former Channel 4 employees, Dennis Ferrier, Jennifer Johnson and Nancy Van Camp.