One league source said he was "95 percent" certain Reid will wind up coaching the Cardinals, and multiple sources stated that he could agree to accept the job by the end of the week.
But another source said the Cardinals' search will be wide open, claiming there is no leading candidate at this time. A source close to Reid insisted that the two sides have not met yet and that a deal is not close.
However, Reid will interview with the Cardinals on Wednesday, a league source confirmed.
The Cardinals formally interviewed defensive coordinator Ray Horton on Tuesday, one day after Ken Whisenhunt was fired following six seasons as the team's coach.
Cardinals president Michael Bidwill also plans to fly to Denver over the weekend to interview Broncos offensive coordinator Mike McCoy.
Reid has spent recent days assembling a coaching staff, telling potential assistants that an announcement could come quickly, according to one assistant. After his run of 14 seasons in Philadelphia ended Monday, Reid appeared set on coaching again next season.
Arizona would be appealing to Reid and his family on a number of levels, none more so than his wife Tammy is from the Phoenix area and it would bring them closer to family.
KTVK-TV in Phoenix reported earlier Tuesday that Reid had emerged as the favorite for the Cardinals job.
In Arizona, Reid also 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 following a trade from Philadelphia in 2011.
In a perfect world, Arizona would get to hire Reid and his offensive staff and match it with Horton and the defensive staff, giving the Cardinals a winning one-two coaching combination.
Kolb, who threw 11 touchdowns and 14 interceptions in four seasons with Philadelphia, remains under contract with Arizona, but the team is expected to want to restructure his contract. He is set to make $9 million plus a $2 million roster bonus for the coming season.
"I'm not ready to give up on Kevin Kolb yet," Bidwill said Monday.
Bidwill has to interview McCoy this weekend in Denver under NFL rules that provide a narrow window for such meetings with members of coaching staffs whose teams have a bye the first round of the playoffs. McCoy also has an interview scheduled with the Browns.
Larry Fitzgerald, who had one of his worst seasons as the Cardinals struggled at the quarterback position, weighed in on the firing of Whisenhunt and general manager Rod Graves. In a lengthy tweet, Fitzgerald thanked the pair for giving him the opportunity to "live my dream in the NFL."
"We all shoulder the blame for a disappointing season which began with such promise," Fitzgerald wrote.
He said that "even in the midst of a tumultuous season, it was still a pleasure to work for the staff we served under, and for that we remain grateful."
"Their professionalism will provide for renewed accomplishments in different environs," Fitzgerald wrote. "We all, to a man, thank them and wish them the best."
Whisenhunt set the record for victories by a Cardinals coach, going 45-51 in six seasons, 4-2 in the playoffs. The team got off to a 4-0 start but lost 11 of 12 to finish 5-11 for the second time in three seasons.
Information from The Associated Press was used in this report.