Reports have suggested Lloris will look to leave White Hart Lane at the end of the season, should Tim Sherwood’s side fail to qualify for the Champions League.
And Giroud has told French TV that the shotstopper would be more than welcome at the Emirates.
Sol Campbell was the last player to make a direct move from Tottenham to Arsenal, signing on a free transfer in 2001, but the clubs do not have a history of doing business together.
“We go out together and talk about everything,” Giroud said.
“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.”
Lloris has established himself as one of the best goalkeepers in the Premier League since signing for Tottenham in the summer of 2012.