Liverpool beat Sterling's City 3-1 on Sunday to move nine points clear of the defending Premier League champions at the top of the table.
The Daily Mail reported that Liverpool defender Joe Gomez and Sterling had to be separated by teammates on Monday after a "physical confrontation".
The pair had also clashed on the field towards the end of Sunday's match.
In a statement issued by the Football Association, Southgate said: "We have taken the decision to not consider Raheem for the match against Montenegro tomorrow.One of the great challenges and strengths for us is that we've been able to separate club rivalries from the national team. Unfortunately the emotions of yesterday's game were still raw".