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Messi was booed and whistled during his side's 3-0 win over Bordeaux last weekend.
It comes after the French giants were dumped out of the Champions League by Real Madrid.
Messi failed to influence the match, with Real securing a spot in the next round of the competition after winning the tie 3-2 on aggregate.
PSG fans aimed their frustration at the seven-time Ballon d'Or winner, jeering his touches against Bordeaux.
And the superstar forward's former Barcelona teammate Alves reckons he's not enjoying himself in France.
"Messi? For me, Leo isn't enjoying himself, for me he's out of place there," he told ESPN via barcacentre.
"I'm going to say something that Leo always told me: 'Where are you going to be better than here', and he's right. I have experienced it."
Alves is hoping Messi returns to Barca. He added: "I hope Messi can come back."
The 38-year-old, who enjoyed a spell at PSG, signed a deal with Barca until the end of the season last November.
He highlighted Pedri, 19, when asked about his current crop of teammates.
"The one who has surprised me the most is Pedri, he is intelligent, he reminds me of Xavi," he explained. "He manages to see things that others don't see and execute things that others can't."
On Messi being subject to jeers, Mauricio Pochettino said he was left upset by the actions of their home supporters.
"Everyone who loves PSG is sad after the disappointment of Madrid," said the PSG boss.
"I’m sad with what I experienced today. We were all affected.
"We understand the disappointment and the frustration. We’re all living it together, as a team.
"We have a duty to take responsibility for what happened. We share this disappointment with the supporters."
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