The news agency claims tensions boiled between the Portuguese duo in the dressing room at half-time of the Black Eagles' Europa League last-16 tie against Atletico Madrid on Thursday, as they fell to a 3-0 deficit, forcing the ex-Braga man to ring the changes.
However, it was Quaresma who would be sacrificed, in favour of wing-back Ismail Koybasi, after a below-par showing in the first-half, and the flanker did not take to the news lightly as he reportedly began throwing water bottles, before launching a stinging attack at his boss.
"I brought you here, you just think of yourself," the former Inter and Barcelona star allegedly said.
"If I was not here, you [Carvalhal] would not be here. You can not remove me from the match because you're nothing."
Nonetheless, the Turks went onto lose 3-1 against Diego Simeone's side in the first leg, but it now appears Quaresma may have played his last game under the current leadership at the Istanbul club if Carvalhal's latest revelation is to be believed.
"As long as I'm at the helm of this team, Quaresma cannot wear the team uniform. I will leave him out of the squad," Carvalhal is quoted as saying.
"The players have heard me say it in front of them - Quaresma is now a closed chapter for me."
He now looks certain to miss the return leg against the Spaniards on March 15, and has also been dropped from the squad to face Orduspor on Sunday, as Besiktas try to build on fourth position in the Super Lig standings.
His future could also be decided in the coming weeks, when the club announce the results of their presidential elections on March 25.