The France World Cup winner, who moved to Old Trafford in 2016 in a £89m deal, has been linked with another big-money move, to Barcelona, following a series of apparent fallouts with United manager Jose Mourinho.
But the 25-year-old was made captain for his club's Premier League opener against Leicester City and was praised by Mourinho for his performance, which included the goal that set United on the way to a 2-1 win.
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However, a post on Pogba's Instagram account shortly after the game fuelled continuing speculation that he is still far from settled at Old Trafford.
In comments widely regarded as reflecting continuing problems with his relationship with the United boss, he wrote: "I'll always give my best for the fans and my team mates, no matter what's going on."
He did not directly mention Mourinho, who has been critical of the player he signed from Juventus in 2016.
But after being asked if he was "happy and comfortable" at United, Pogba replied: "There are things I can say and there are things I cannot say... otherwise I will get fined."
He adds: "When people trust you, then you're good in your own head, and it's going to be easier.
"I always give my best for the fans, for the team mates ... and for the people that trust me."
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