The latest defeat, a 2-0 loss at Salzburg in the Europa League on Thursday, means even victory against Athletic Bilbao in the final round of matches may not be enough to see them advance to the knockout stage of the tournament.
Before Thursday's setback, they Qatari-backed side slumped to consecutive defeats in Ligue 1, including a 3-0 loss to bitter rivals Olympique Marseille, to slip from first to second in the standings.
The series of results has heaped pressure on Kombouare, with former France international Claude Makelele, an advisor to general manager Leonardo, rumoured in the media to be poised to take over on a caretaker basis.
"We're still building [the team], and you don't build a team in four months," Kombouare was quoted as saying by sports daily L'Equipe on Friday.
PSG spent over 80 million euros on new players before the start of the season, among them Argentine sensation Javier Pastore, who joined from Palermo for a French record 42 million euros.
Following an impressive start to the season, however, PSG have struggled in recent weeks, but Kombouare remains resolute.
"We have to be able to react," he said. "I am a fighter and I want to fight. My future? Ask the club's officials."
Makelele, who retired at the end of last season, hinted that Kombouare should not feel threatened.
"Antoine Kombouare is the PSG coach. I have always been behind him, he has my total support," he told L'Equipe.
"Me, [as] coach? No comment," he added.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
