Reports suggest Lloris would seek an exit from White Hart Lane should Tim Sherwood's side fail to qualify for the Champions League this season and Giroud told French TV he would be welcome at the Emirates.
Sol Campbell was the last player to cross the divide directly when he joined the Gunners on a free transfer in 2001, but the two rivals do not have a history of doing business together.
However, Giroud said: "We go out together and talk about everything.
"We talk about life and sometimes the French team a bit and our wish to have a great experience together at the World Cup.
"Have I asked him (Lloris) to join Arsenal? Yes, I have with Lolo (Laurent Koscielny). He would have liked to, he would quite like to. You will have to ask him the question."