For much of the summer Lyon captain Fekir looked on the brink of joining Liverpool from Lyon only for the move to collapse following advanced talks.
Maurizio Sarri is still looking to bring in outfield players before the transfer window closes and the Blues are weighing up a move for the 25-year-old.
"I spoke to him when we were together in the French national team, when his move to Liverpool fell through," Giroud told Foot Mercato.
"Then we discussed Chelsea, and I even think that Eden (Hazard) 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."