Egypt lost their first two games against Uruguay and hosts Russia, crushing the hopes of fans that prolific striker Mohamed Salah, despite his recent shoulder injury, would lead the Africans into the knockout stages.
Instead, their campaign will peter out against Saudi Arabia, who also head home after Monday's match in Volgograd having lost both their opening games too.
"I have never excluded anything. It might be my last game and it might not. It will depend on a number of factors," Cuper, who was named Egypt coach in 2015, said when asked by reporters about his future.
"Of course I would like to make everybody happy, to come up with something that everybody would agree with. But it's impossible," the Argentine said.
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While saying there had been "small disagreements" within the Egypt camp, Cuper added that he would not respond to questions about whether captain Essam El-Hadary had fallen out with the rest of the team.
"There might be small disagreements but I would like to hear evidence or proof of this," he said. "If you don't have evidence or proof, I won't answer that question."
El-Hadary, who was not included in the starting team for either of Egypt's first two games in Russia, denied any rift.
"If I had been making trouble in the team then I don't deserve my spot on the team. That's my simple answer," the goalkeeper said, sitting next to Cuper at a news conference.
El-Hadary said he was hoping to get the nod for Monday's match which would make him the oldest ever player to appear at a World Cup at 45 years of age.
"Obviously I will be very happy if I play in the match tomorrow. But that is not certain and that choice will be made by the management of the team," he said. "This world record will be my achievement but it will also be an achievement for Egypt."
(Writing by William Schomberg; Editing by Christian Radnedge and Ian Chadband)
