Sterling went head-to-head with the Liverpool center back on Sunday in City's 3-1 loss to the Reds at Anfield, and couldn't leave the tension with his club.
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.
[ MORE: Liverpool 3-1 Man City ]
Ex-Liverpool winger Sterling played physical on Sunday and was confrontational on plenty of occasions, too, including a heated exchange with Gomez late in the contest.
Wild stuff, and a bad look for Sterling. He's been England's best player for some time, and the club is on the verge of qualifying for EURO 2020 but hasn't achieved that goal yet.
England hosts Montenegro on Thursday and visits Kosovo on Sunday.
Where does this leave Sterling in the England set-up? He's one of the best attackers in the world, but Southgate runs a tight ship and the Three Lions will likely qualify without him (and there are plenty of English wingers who will queue up for the job). He'll get another chance almost surely, maybe even on Sunday, but there's a slippery slope.