The White House, however, would not confirm the report.
Both Valerie Jarrett, Obama's senior advisor, and Press Secretary Robert Gibbs told NBC there has been no change in the president's status.
Obama staffers recently told reporters the White House was sending an advance team to Copenhagen just in case Obama can go.
Last week, both the president and Michelle showed their support for Chicago's bid during an Olympic and Paralympic demonstration on the White House South Lawn.
Also attending: 26 Olympic and Paralympic athletes, including two-time Olympic heptathlon champion Jackie Joyner-Kersee of East St. Louis; reigning Olympic decathlon champion Bryan Clay; two-time intermediate hurdles champion Edwin Moses; and Michael Johnson, the only man to win the 200 and 400 meters at the same Olympics.