Reports out of the UK claimed Fernandinho and Kompany were involved in a heated half-time row during City's 2-1 loss to Liverpool at Anfield last month.
The pair were dropped from the starting line-up for the fixture against Leicester City three days later, but the Premier League champions denied a dressing-room spat was the reason behind their axing.
Fernandinho has now moved to dispel those reports, claiming there was no fight.
"People are creating and telling stories, even though it didn't happen that way," the Brazilian told the Manchester Evening News.
"It was nothing major. There were other people around us, and you have to raise your voice a little bit. There was no fight, just a conversation.
"Every player in every team speaks to each other in order to improve the quality on the pitch – that communication is necessary. You have to talk, and that is what happened.
"There was a conversation and not much more than that. I don't know why people actually thought there was a fight. We spoke about how we could improve things in that match."
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