Koscielny is facing a fine after refusing to go on their pre-season tour of the USA because the Gunners refused his transfer request.
The 33-year-old has faced fierce criticism from fans and pundits since, but fellow Frenchman Giroud, his former team-mate, says Koscielny has always been respectful of the club.
Giroud said: “You cannot make a judgement when you don’t have all the clues. I’m pretty sure we don’t know everything in this situation.
“I hope both sides will find the best agreement. Lolo is a good friend of mine. I’ve known him now for 10, 11 years. We played together in the second division [in France, at Tours].
“He’s been playing for Arsenal for nine years; he’s been the skipper for so many years – very respectful, very professional, always the best example for the young players.
“The club gave him the opportunity to play at Arsenal, and it was a big, big opportunity for him to show his quality in the Premier League.
“I think he has always been grateful about that and respectful to the club. I don’t understand how we have got to this situation.
“I feel very sad for him because he’s a great person and the media wants to give a bad image of him.
“I don’t know what really happened – but one thing for sure is Lolo is very hurt by what’s happening and he’s an emotional person”
“I’m not at the club, I don’t know what really happened – but one thing for sure is Lolo is very hurt by what’s happening and he’s an emotional person.”
Koscielny insists he was given verbal assurances he could leave Arsenal for free this summer but the club deny this and want a £9m fee to release him.
That put off Borussia Dortmund and is also proving a problem for Rennes and Bordeaux, who both want to take the defender back to his homeland.
Koscielny, who has made 353 appearances since joining Arsenal from Lorient for £10m in 2010, is training in London.
Gunners boss Unai Emery, speaking after his side’s 3-0 win over Colorado Rapids, said: “Now it’s a matter for him and the club.
“They need to speak and are speaking about his situation. I’m waiting on his conversation and decision.”