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.
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.
The claim will be sure to upset Spurs fans, just as they attempt to push forward and challenge Liverpool for the final Champions League qualification spot this season.
Lloris is a goalkeeper with a burgeoning reputation and has achieved 10 clean sheets this season in his 24 Premier league matches, per Squawka.
The French players based in London are good friends and have been spotted out together via 101GreatGoals:
However it is unlikely that the Gunners would move for a player given the faith that Arsene Wenger has shown in Wojciech Szczesny.
However, would Lloris improve Arsenal?
Looking at the statistics, the answer would appear to be no. Szczesny has more shutouts than Lloris, per Squawka, and is without doubt still improving.
At 27 years old, Lloris is still relatively young in goalkeeping terms, but the move would not make sense given Arsenal's need in other parts of the pitch.
The main stinging point though of Giroud's comments will be for the supporters and circles back to a question of faith, loyalty and devotion. You only have to think back to Sol Campbell's acrimonious switch in colours, to the red of Arsenal, to remember just how much these sets of fans hate each other.
There is no way that Daniel Levy would sanction such a move, if only on the grounds of keeping his own supporters content. Lloris has not been a wild success at White Hart Lane, but he is slowly winning people round.
If he demands a move because Spurs do not reach the Champions League, that also would be a surprise. His ambitions might be to compete at the highest level, but Tottenham appear to be the correct platform for his talents at present.
However, there is a chance that should the goalkeeper have a fantastic World Cup, and help his country progress deep into the tournament, that his stock could dramatically rise. This fact on its own could facilitate a move away from Tottenham, and alert bigger clubs if he wanted a transfer of any kind.
But a move to Arsenal would be monumental, and something we are surely unlikely to see.