Detective Rick Wall said two of McGregor's associates couldn't get in touch with him and that someone entered his room at the hotel in downtown Salt Lake City and found the 48-year-old McGregor unconscious Tuesday morning.
Police were called about 9 a.m. MDT and emergency workers arrived on the scene and were unable to revive him.
"There are no signs of foul play. ... Based on the initial investigation (police and fire officials) did not see anything suspicious," Wall said. "There is nothing suspicious. At this point it would look like it was some sort of a natural cause or something along those lines."
Wall said the investigation has been turned over to the medical examiner's office, which will determine the exact cause and time of death.
The Rockies said McGregor was on a business trip with team chairman and CEO Charlie Monfort and executive vice president Greg Feasel.
"Words cannot describe the level of shock and disbelief that we all are feeling this morning at the loss of Keli," Charlie Monfort said in a statement. "Our thoughts, our prayers are with Lori and the entire family as we all try to cope and understand how such a tragic loss could occur with such a wonderful man."
McGregor is survived by his wife, Lori, three daughters and a son.
Chief Medical Examiner for Utah Todd Grey told The Associated Press Tuesday that state law says the records of the medical examiner are considered confidential. He said that his office cannot comment on the specifics of any case without a release from the next of kin.
McGregor, 48, was in his 17th season with the Rockies, his ninth as club president. He began his career with the Rockies in October 1993 as senior director of operations. He was promoted to senior vice president in 1996 and executive vice president in 1998.
A two-time All-American tight end at Colorado State, where he ranks fifth on the school's all-time receptions list, McGregor was selected by the Denver Broncos in the fourth round of the 1985 NFL draft. He played for the Broncos, Colts and Seahawks during his brief pro career.
He joined the Rockies in 1993 after a four-year stint as an associate athletic director at the University of Arkansas. He also was an assistant football coach for two years at the University of Florida from 1988-89, where he earned his Master's degree in education with an emphasis on athletic administration.
McGregor, who was born in Primgahr, Iowa, was voted to Colorado State's all-century team in 1992 and was named to the CSU Hall of Fame in 1996.