Allen was waived by the Chiefs on Tuesday, freelance NFL writer Howard Balzer reports.
Allen was claimed off waivers by the Chiefs, Field Yates of ESPN reports.
Allen signed a contract with the Bears on Friday.
Allen (undisclosed) reverted to injured reserve after clearing waivers Thursday, Josh Katzenstein of The New Orleans Times-Picayune reports.
Allen was signed to the Saints' active roster Saturday, NOLA.com reports.