The incident happened around 10 o'clock near 400 E and 600 S.
Police said they were notified of the incident after dispatch received a call from a witness, who reported two men were arguing in the middle of the street.
One of those men is accused of getting into an SUV and hitting the other man before driving the street. Officers found the SUV in a driveway about half a block away.
"The car pulled into the registered address for the vehicle, but we don't at this time believe that the other registered owner was the one in the vehicle," said Lt. Scott Smalley, SLCPD.
Police reported they are still looking for two people who got out of the SUV. At least one suspect could face a charge of aggravated assault with a vehicle.
Anyone with information that could aid Salt Lake City Police in their investigation is urged to call 801-799-3000.