The Telegraph says they had to be pulled apart by stunned team-mates following the altercation at St George's Park.
Other England players had to jump in and end the physical confrontation on Monday afternoon.
It is understood the argument started when 'banter' about the Reds win over City got out of hand.
Sterling hs been dropped from the starting XI for the Montenegro fixture this Thursday after a team meeting.
He apologised to Gomez in person, along with the rest of the squad which saved him from being sent home.
An England statement said: "The FA can confirm Raheem Sterling will not be considered for Thursday's EURO 2020 qualifier against Montenegro as a result of a disturbance in a private team area at St. George's Park today.
"He will remain with the squad."