Lacazette was on target while Partey excelled in midfield as Arsenal overcame Wimbledon 3-0 to set up a fourth-round meeting with Leeds United.
But according to Arsenal journalist Chris Wheatley, he caught the pair in an explosive chat at half-time.
He said on his YouTube channel: “When the players were actually going into the tunnel, I noticed a fairly heated discussion between Alexandre Lacazette and Thomas Partey.
“It looked like Lacazette was maybe a little bit frustrated; perhaps he was isolated upfront.
“Of course, he did score from the penalty spot, but I don’t think it was the best performance from Lacazette against Wimbledon. And clearly, there was a talk on the stroke of half-time between the two players.
“I’m not quite sure what it was about, but Lacazette was fairly animated in terms of throwing his hands up in the air, shrugging his shoulders.”
Partey retained his place in the starting lineup for Sunday’s impressive win over Tottenham. The French attacker on the other hand was left on the bench.