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The Catalan giants are currently ninth in La Liga and bottom of their Champions League group, with Koeman under intense pressure at the Camp Nou.
Koeman has lost a number of senior players, including Lionel Messi, and he's said to be unsure of club legend Pique.
Pique has been vocal about his disappointment in the club's performances this season and is particularly in post-match interviews.
He was also seen arguing with Sergio Busquets during Saturday's 2-0 loss to Atletico Madrid.
Speaking after the defeat, Pique didn't hold back at all.
Pique said per Marca: "We could play for three hours and still not score."
The World Cup winner also opened up on his spat with Busquets and explained: "We had spoken about when [Thomas] Lemar lays the ball off and Joao Felix runs forward they outnumber you and someone has to follow him.
"But this is the nervousness that comes in these situations.
"This is the result we didn't want but we have to rest now in the break and come back strong.
"We were brave but they scored from very little. All we can do is to keep fighting. The two goals are very similar in that they come at us with numerical superiority."
Koeman has also chosen to sell Luis Suarez to Atletico Madrid in his spell - something that's come back to haunt him.
Suarez thinks the entire club is currently in crisis and has urged former player Xavi to NOT take the job.
"As a soccer fan and what he has done as a player, I don't think that today, tomorrow or the day after is the time to catch the team," the Uruguayan international told SPORT.
"He is intelligent and knows the difficulty of the club. He must wait for the moment. He has colleagues inside with whom he will have to make decisions and it will be difficult."
Suarez was told he wasn't 'wanted' in Catalonia and moved to Atletico, helping them win La Liga in his debut campaign.