Enrique, meanwhile, may end up at Chelsea instead.
And Transfermarketweb say those developments may lead to Emery taking the Arsenal job.
Meanwhile, speaking last month, the PSG manager tipped Wenger to replace him at the Parc des Princes.
"Every year we have a meeting in Nyon with 12 European coaches. And it's a reference for us,” he said.
"When we're there, everyone wants to hear what he says because it's a great reference for football.
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Arsenal news: Arsene Wenger has managed his last game for the Gunners
Wenger signs off Arsenal career with win against Huddersfield
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“He brought a lot of positive things into the teams he coached, including Arsenal.
"He was there a long time. He spoke well of me when we spoke together. He gave me his support.
“I have an admiration for him as a person, but especially as a coach.
"He is a coach who has the ability, quality and experience to coach all the best teams in the world.
“And the PSG is one those teams. So he would be able to train PSG."