Chiefs chairman Clark Hunt was meeting with Reid in Philadelphia, a person familiar with Reid's plans told The Associated Press. The person spoke on condition of anonymity because the plans were not made public.
ESPN.com first reported the interview would take place.
Reid, fired Monday after 14 seasons in Philadelphia, also planned to interview for the open job in Arizona. The Cardinals dismissed Ken Whisenhunt on Monday.
The Chiefs have a connection with Reid through team president Mark Donovan, who spent his previous six years as the Eagles' senior vice president of business operations.
Hunt began his search for Crennel's replacement in Atlanta, where he interviewed offensive coordinator Dirk Koetter on Tuesday. But one day later, Falcons coach Mike Smith said Koetter had signed a new contract and would not be pursuing a head coaching job this season.
"I don't want to really get into any of the details," Smith said Wednesday. "Dirk is going to be here with us. He informed me of that last night. We talked at length."
Hunt told the AP in an interview this week that he would lead the search for the Chiefs' next coach, not embattled general manager Scott Pioli. Hunt said he had "the appropriate resources available to help me in the process," but would not say who is assisting in the search.
"We're very well organized," Hunt said. "We want to be thorough, but efficient as well."
Hunt's decision to spearhead the coaching search coincides with his plan to take greater control of football operations. Pioli had been responsible for all personnel moves since he was hired in 2009, including the hiring and firing of head coaches.
Pioli parted with Herm Edwards shortly after he was hired and replaced him with Todd Haley, but their relationship was strained. Haley was dismissed in December 2011 and Crennel was made interim coach. He was given the job on a permanent basis in January.
Crennel was fired Monday after going 2-14 in his first full season.
It was widely thought Pioli would also be fired after a series of failed drafts and poor free-agent acquisitions. Hunt said he had not decided whether to release the GM.
It's likely that the decision won't be made until Hunt hires a coach.
"I don't have a timeline laid out per se on that," Hunt said. "Obviously the beginning of February there are a lot of important events related to the upcoming draft, the combine and so forth, and we want to be solidified in that regard before that."
The Chiefs have the No. 1 pick in the NFL draft for the first time in franchise history.
Hunt refused to discuss potential candidates to replace Crennel, but did offer a lengthy list of qualities he's seeking in an ideal head coach.
"I'd say a proven leader," Hunt said. "Somebody who has demonstrated the ability to build a successful program, or been part of building a successful program. Somebody of high integrity, somebody who is a successful teacher and communicator. Somebody who has a high football IQ, but at the same time likes to roll up their sleeves and work hard."
Reid would appear to have most of those qualities.
The Eagles were 3-13 the year before he arrived, but two seasons later, they went 11-5 and finished second in the NFC East. It was the first of five straight years in which the Eagles won at least 11 games, and included a trip to the Super Bowl after the 2004 season.
Reid was 130-93-1 in Philadelphia, the most wins in franchise history. He helped the Eagles win 10 playoff games—the Chiefs haven't won one since 1993—and six division titles.
Reid is considered a bright offensive mind with success developing quarterbacks, an area of particular need in Kansas City. His best years coincided with Donovan McNabb's best years, and the 54-year-old coach also worked with Brett Favre early in his career in Green Bay.
"I'm not going to go into discussing who we're talking to," Hunt said Monday, before adding: "We do have a list of candidates who are priority for us."
AP Sports Writers John Wawrow and George Henry contributed to this story.