The French striker has been strongly linked with a move away from the Gunners with Everton and West Ham said to be chasing his signature.
Giroud has admitted he is not sure if he will be at Arsenal next season following the £52million arrival of Alexandre Lacazette.
But Pires is hoping the striker is ready to challenge for a starting spot in Arsene Wenger's side.
"It will be very difficult for Olivier Giroud but I think he’s a big professional,” Pires told talkSPORT.
Olivier Giroud and Alexandre Lacazette are fighting for a starting spot at Arsenal Arsenal accidentally leak their new away kit Sun, July 16, 2017
Arsenal have accidentally leaked their new away kit before its official launch!
Play slideshow 1 of 8
It’s not easy for Olivier because in one year he will want to play in the World Cup with France, but he is a big professional for Arsenal and it’s better if he stays
“Competition is very important for strikers so I hope Giroud will stay at Arsenal because he’s really important and he scores a lot of goals during the season, but I don’t know what will happen at the end of the market.
“It’s not easy for Olivier because in one year he will want to play in the World Cup with France, but he is a big professional for Arsenal and it’s better if he stays.”
Lacazette arrives at Arsenal after scoring 100 goals in 203 league games for the French outfit as he looks to impress in the Premier League.
The 26-year-old is set to lead Arsenal's line next season and Pires believes he could even follow in the same footsteps as legend Ian Wright.
Get Quotes on Home Insurance
Robert Pires believes Olivier Giroud should stay and fight for his place at Arsenal
“I hope [it’s true] for Alexandre Lacazette because everyone knows Ian Wright was a very good player. I hope Lacazette follows the same way," Pires added.
“I think he is a little bit similar, he’s a striker, he’s fast, he has good ability, and he has scored a lot of goals with Olympique Lyonnais.
“Now, of course, he is not in the same team, he doesn’t have the same partner, he isn’t in the same country, and it isn’t the same football – everything has changed around him so. But I think he is a very good signing.”