Reid said via text the meeting went very well.
Reid also said via text that his interview with the Cards, originally scheduled to begin later Wednesday, has been pushed back, either to Thursday or Friday.
Reid met Wednesday with Chiefs owner Clark Hunt, team president Mark Donovan and general manager Scott Pioli. Donovan spent the 2003 through 2008 seasons with the Eagles, serving as senior vice president of business operations.
Reid, fired Monday after 14 years as head coach of the Eagles, immediately surfaced as a candidate with the Cards, who fired head coach Ken Whisenhunt after six years, and the Chiefs, who fired head coach Romeo Crennel after one full season and three games of 2011.
Reid had arrived in Phoenix by late Wednesday, but it wasnt clear exactly when his meeting with the Cards would begin.
The Cards have already interviewed their own defensive coordinator, Ray Horton, for their head coach vacancy, and are also reportedly planning to meet with Broncos offensive coordinator Mike McCoy. Lovie Smith, fired after a 10-win season with the Bears, has also been mentioned in conjunction with the opening.
No other candidates have been reported to have interviewed with the Chiefs so far. The length of the Chiefs interview with Reid is certainly a strong indication he could be at the top of their wish list.
Reid won more playoff games during the nine-year stretch from 2000 through 2008 (10) than the Chiefs have won in their 53-year history (eight). The Chiefs havent won a postseason game since 1993, when Joe Montana took them to the AFC Championship Game.
Reid also won more postseason games with the Eagles than the Cards have won in their 93-year history (six), although the Cards did beat Reids Eagles in the 2008 NFC Championship Game.
Chiefs Vice President of Media and Marketing Rob Alberino spent the 1997 through 2009 seasons with the Eagles, where he started the Eagles Television Network and won 39 Emmys in his 13 years.
Alberino, one of the Chiefs top front-office executives, tweeted about Reid early Thursday morning: No scoop. Just reminded of some awesome years. Whatever direction we go, I'm on board. Whole town just wants to win. Loving that.