The Gunners striker has revealed he attempted to lure his France team-mate to the Emirates Stadium before he eventually switched to bitter rivals Tottenham instead.
Sissoko signed for Tottenham on transfer deadline day in a deal worth a reported £30m, having initially appeared set for a switch to fellow Premier League outfit Everton from Newcastle United.
The 27-year-old had previously expressed a desire to seal a move to Arsenal in the past and Giroud has since confirmed he spoke with the midfielder regarding a move to the Emirates Stadium.
“I told him to give Arsenal the priority. It’s true it was special denouement. Until the end he didn’t know what he’ll do,” Giroud said.
“It’s good for him. I think it was quite a long month for him so it’s good that something could have happened even in the very last moments. It’s great for him.
“Tottenham is a great team in our league. Obviously we all wanted for him after his good Euro and great performances, that he joins a premier League club. In the Premier League Tottenham are an opponent for the trophy this year. I hope he will not be in good conditions against us.”
Giroud also spoke of his excitement ahead of Arsenal’s clash with Paris Saint-Germain in the Champions League group stage and that he hopes to regain a first-team place in Arsene Wenger’s team.
The 29-year-old has only turned out once in the Premier League so far this season – a 78th-minute substitute appearance in the goalless draw at Leicester City in week two.
“If I am underestimated, I’m not sure but I started the season on the bench because I came back from holidays the ninth of August. I wasn’t in the group for the first game. For the second game I came in with only two days of training in the legs. It seems then a logical choice,” he added.
“For the last game I should have come in but a player got injured so I didn’t and that’s it. After two weeks of preparation a player cannot be ready. That’s why I started on the pitch.
“Gradually I hope to play more and find my fitness back. Like the last season as easy as that. It’s just a question of preparation I’m not more worried than that.”