Reid did not make a scheduled trip to Arizona on Wednesday night, sources told ESPN's Adam Schefter. It was not clear why he did not fly out as scheduled after meeting with the Chiefs.
The Chiefs, looking for a new coach after firing Romeo Crennel on Monday, were in Atlanta on Tuesday to interview Falcons offensive coordinator Dirk Koetter before flying off to Philadelphia to meet with Reid on Wednesday.
On Wednesday, the Falcons announced that Koetter would not pursue a head-coaching position this offseason.
Reid has been assembling a coaching staff, telling those coaches he believes the process of finding a new position could be settled this week.
The Cardinals fired coach Ken Whisenhunt on Monday. Team president Michael Bidwill interviewed Cardinals defensive coordinator Ray Horton on Tuesday and plans to fly to Denver this weekend to interview Broncos offensive coordinator Mike McCoy.
Bidwill has identified Horton, Reid and McCoy as candidates to replace Whisenhunt, who was dismissed after six seasons.
Speaking to Azcentralsports and Fox Sports Arizona afterward, Horton said the Cardinals job easily would be his top choice.
"For a number of reasons," Horton said. "I like the organizational structure and then I love the fan base. For me, it's been an amazing fan acceptance of me, whether at the game or on the street. That plays a lot, where the community appreciates what you do."
The Cardinals will also interview Redskins pro personnel executive Morocco Brown for their vacant GM spot Friday in Washington, according to a league source.
Some reports have said that Reid and the Cardinals are close to a deal, including one league source who told ESPN he was "95 percent" certain Reid would end up with Arizona. But another source tells ESPN the Cardinals' search will be wide open and that there is no leading candidate at this time.
In Arizona, Reid could try to help salvage the career of former Eagles quarterback Kevin Kolb, who has struggled since signing a lucrative five-year deal with the Cardinals after a trade from Philadelphia in 2011. Kolb showed promise as a backup with the Eagles under Reid.
Reid was fired by the Eagles on Monday after 14 seasons with the franchise.
ESPN NFL Insider Adam Schefter and The Associated Press contributed to this report.