The Mirror says Sterling warned Gomez 'don't f**k with me' during their heated exchange in Sunday's Premier League game.
The pair clashed towards the end of City's 3-1 Anfield loss to Liverpool.
Professional lipreader Tina Lannin of 121 Captions has offered her interpretation of the exchange.
As Raheem is pushed by Gomez he walks straight back into Gomez and says: "Don't f**k with me, Joe. Don't f**k with me."
Gomez responds by saying "come on!" before he's pulled away by fellow Liverpool players.
The pair clashed again 24 hours later, in the canteen at England's St George's Park training base which led to Gareth Southgate axing Sterling.