The experienced right-back has just one year left on his contract with the Ligue 1 champions.
Both Premier League sides are looking at Meunier as an economically viable summer signing.
Arsenal want stronger competition for Hector Bellerin than Stephan Lichtsteiner proved capable of providing last season.
Manchester United boss Ole Gunnar Solskjaer does not trust Diogo Dalot as his number one right-back yet.
But both teams may be forced to turn their attention elsewhere after hearing what Meunier had to say on his situation.
Speaking about his future to RTBF, the Belgium international said: “I will repeat myself again: my ambition is to stay in Paris.
“If they want me, that will be even better – we will be hand in hand. If they do not want me, then we will find a solution.”
United have had a £40m bid for Crystal Palace full-back Aaron Wan-Bissaka turned down in recent days.
The Red Devils are also keeping tabs on Norwich youngster Max Aarons in case they cannot do a deal with the Eagles.
Meunier remains Arsenal’s main option and would set them back between £20m and £25m if they can persuade the player to join.
“Unai Emery has been in touch with him a few times because a right-back is a priority at Arsenal,” Belgian transfer expert Kristof Terreur told Sky Sports’ Transfer Talk podcast.
“His agent has also had a meeting with Everton too but there has been nothing concrete so we are just waiting.
“PSG want to sell him though for the right price at £20-25 million.”
Meunier’s recent words contradict what he reportedly told Le Parisien last week.
“It’s something that could suit me,” he said when asked about a move away from PSG.
“I don’t think the club would make a lot of money from me, actually. I have a market value, but I’m a defender, I play one game out of three and I’m turning 28.”