The Daily Mail's Matt Hughes and Sami Mokbel report that Sterling tried to grab Gomez by the neck at St George's Park on Monday.
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The bust-up is said to have left the England squad shocked after what was initially a playful back-and-forth quickly escalated into a physical confrontation between the two standouts.
In an announcement on the official web site, the FA wrote: 'We can confirm Raheem Sterling will not be deemed for England's EURO 2020 qualifier in the direction of Montenegro as a finish results of a disturbance in a personal group house at St. George's Park these days. "He will remain with the squad".
"One particular of the great difficulties and strengths for us is that we have been equipped to individual club rivalries from the countrywide crew".
The pair clashed at Anfield on Sunday during Liverpool's 3-1 win over Manchester City and the City man looked to reignite the spat over the global break.
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'My feeling is that the right thing for the team is the action we have taken.
Gareth Southgate is set to give James Maddison his England debut in one of this week's clashes against Montenegro and Kosovo.
Sterling has been in impressive form for England during their qualifying campaign, scoring eight goals and providing five assists.
"Now that the decision has been made with the agreement of the entire squad, it's important that we support the players and focus on Thursday night". He will miss their last home qualifier for Euro 2020 and the chance to advance, plus the team's 1000th fixture.
England are on the verge of qualifying for next year's tournament and face Kosovo in Pristina on Sunday after their clash with Montenegro.
Sterling has earned 55 caps for England, having scored 12 goals as a senior worldwide.