Wenger recently celebrated 20 years in charge at Arsenal, during which time he has won three Premier League titles and the FA Cup on six occasions.
The Frenchman is out of contract at the end of this season, though, with speculation continuing to mount that 2016-17 will be his last at Emirates Stadium.
Wenger has been linked as the permanent successor to Sam Allardyce with England, although Pires does not think international management would suit his former boss.
"I think he'll stay, but it's true that the English national team wants him," said Pires, who played a key role in Arsenal's title winning sides of 2002 and 2004.
"But I'm saying that because, and it's just my opinion, he loves to be on the pitch every day. When you're managing a club or a national team, it's not the same thing.
"So this is why I think he'll stay at Arsenal, because he loves to be on the pitch every morning.
"They think he would be the ideal person to manage this team because this team needs energy and stability, and especially to be credible. With what happened, I think England is not credible anymore.
"If they pick Arsene Wenger, knowing he's a great coach, he speaks English very well, he has a good persona, so yeah he would be the perfect man.
"But I know a bit [about] Arsene, he loves his club Arsenal, he built many things in this club… I know his contract is ending, I don't know what will happen, but for me the best thing would be for Arsene to continue at Arsenal."