Multiple reports said Reid and the Chiefs were working out the final details of a contract. The NFL's website said Reid's agent was in the process of canceling interviews that had been planned with other teams searching for a new coach.
Similar reports had circulated Tuesday that Reid was bound for the Arizona Cardinals where Ken Whisenhunt was fired.
Seven of the league's head coaches from the 2012 season were fired this week and Reid was one of them, having lost his job Monday after spending 14 seasons with the Eagles.
He led Philadelphia to nine playoff and five NFC championship appearances while becoming the winningest coach in franchise history at 130-93-1. The Eagles faded to a 4-12 record this season and finished last in the NFC East.
Kansas City dismissed Romeo Crennel Monday after the Chiefs struggled to a 2-14 campaign. The Chiefs will own the No. 1 selection in the 2013 NFL draft.