Earlier in the day, a league source familiar with the situation told The Associated Press that doctors were still trying to determine the extent of a health problem that forced one interview to be pushed back.
The person spoke to the AP on condition of anonymity because details of Arians' illness have not been made public by the team.
Mike Brown, Arians' agent, denied there had been any change to Arians' schedule.
Arians, a 60-year-old prostate cancer survivor, has been complaining of dizziness and migraine headaches, conditions doctors believe is related to an inner-ear infection, the person told the AP.
Five NFL teams are looking for head coaches. The Colts have given at least three teams permission to speak with Arians: the Chicago Bears, Cleveland Browns and Philadelphia Eagles.
The San Diego Chargers are also believed to be interested in Arians. They hired Tom Telesco, Indy's vice president of football operations, as their new general manager on Wednesday.
Arians took over the team after head coach Chuck Pagano was diagnosed with leukemia in September.
Under Arians, the Colts went 9-3 and clinched their first playoff berth of the post-Peyton Manning era. The nine victories tied the NFL record for most wins after a midseason coaching change and immediately created speculation about Arians' future plans as well as the possibility of him winning the league's coach of the year award.
Pagano returned for the final week of the regular season and shared a bear hug with Arians, a longtime friend after an emotional win over Houston.
But when Arians showed up for Sunday's team breakfast in Baltimore, he said he felt ill and was taken to the hospital. Quarterbacks coach Clyde Christensen called the plays in Arians' absence, a late adjustment that made a bigger impact than anyone acknowledged after the game.
"It's a big deal that Bruce got ill out there, it really is," the person told the AP. "It's not a side note. It's a major happening, it's major adversity that you have to deal with."
Arians was released from a Baltimore hospital on Monday evening after his blood pressure stabilized, but has been under doctor supervision since then. He was medicated for the return flight to Indianapolis and taken immediately to an Indy hospital by ambulance, the person said.
Pagano, rookie quarterback Andrew Luck and other Colts players have repeatedly said they would like Arians to stay in Indy, though they understand why he would leave for another team. But they certainly didn't want a health problem derailing what could be Arians' last best chance to fulfill his lifelong dream of becoming an NFL head coach.
Arians has said he will listen to other offers, though he is happy in Indianapolis. The Colts are expected to give him a pay raise and a new job title if he returns next season.
Clearly, things weren't the same without Arians during Sunday's 24-9 loss to the Ravens.
"I don't think people realize how unsettling all that was for Andrew (Luck)," the person said. "As a rookie in a playoff game, to all of a sudden have Bruce gone. That's the guy who is talking in your ear, and then you're in the playoffs and all of a sudden that's gone. It's a big deal."
Arians has mentored the likes of Manning, Ben Roethlisberger and now Luck. He won two Super Bowls as an assistant in Pittsburgh, served on Paul "Bear" Bryant's staff at Alabama and has had a big part in two of the biggest turnarounds in NFL history—the 10-game improvement of the 1999 Colts and Indy's nine-game improvement this year.
His only previous head coaching experience came during a six-year tenure at Temple in the 1980s.