On air traffic control radio captured by the website LiveATC.net, the tower can be heard telling the pilot of the 737 to "go around" and circle the airport.
The controller told the ERJ to watch out for the larger plane on the right.
"Yeah, we were putting the nose down, and, uh, he was real close," the pilot responds.
The 737 flew 135 yards away vertically and 50 yards away laterally from the smaller regional jet.
"We are working with the NTSB in its review of the incident," United spokeswoman Christen David told CNN.
There was no damage to either aircraft or any injuries, according to the NTSB.
The agency will not make a determination of what caused the incident until it releases its final report, which is expected to take months.