Fekir has been linked with a move away from his current employers all summer, with Liverpool almost reaching a deal for the French international in June.
Speaking to Foot Mercato, however, Giroud said that alongside teammate Eden Hazard, the pair attempted to convince Fekir to entertain a move to Stamford Bridge.
"I spoke to him when we were together in the French national team, when his move to Liverpool fell through," the Chelsea forward said. "Then we discussed Chelsea, and I even think that Eden said a couple of words to him.
"We would obviously welcome him, he is a super player, but I don't know if this is something that could happen as the window closes on Thursday."