It is currently in vogue for club legends to return to their former homes after Henry on Monday marked his second debut with a winning goal against Leeds.
Paul Scholes has come out of a short-lived retirement to help Manchester United for the remainder of the season and played in the weekend's FA Cup win over Manchester City.
It has been rumoured Pires could sign a short-term deal with Arsenal because he is training with Arsene Wenger's club, but the 38-year-old has dismissed the claims.
Asked about the prospect, the 2001/02 English Football Writers' Association's Footballer of the Year told L'Equipe: "No, that is for sure.
"It is absolutely not my intention nor the one of Arsene, who is already 'full' in the midfield.
"What is nice with English clubs is the fact they have respect for former players. What happened with Henry, or Scholes at Manchester United, has not surprised me.
"The beautiful story between the Gunners and Henry is going on. Not mine."
Former France international Pires, a two-time Premier League champion and three-time FA Cup winner, has been a free agent since May after leaving Aston Villa.
It has been suggested the World Cup winner and European champion will retire, but he claims to have been a target of Ligue 1 side St Etienne and is now considering offers from China and India.
"I am waiting for propositions from Asia," he said. "Nowadays the new destination is China. I am on the negotiation level.
"I have also first contact in India. That is cool. That would be a nice destination on every level.
"I am waiting to see what could happen with China later in January. As its league will resume soon, it should not last too long. If I have nothing else at that moment, I will stop."