The duo are team-mates with the French national team, but ply their trade on opposite sides of the North London divide domestically.
However, Giroud has teamed up with Arsenal defender Laurent Koscielny - also a France international - in an attempt to persuade Lloris to make the controversial switch.
"We go out together and talk about everything," he is quoted as telling French television. "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 to join Arsenal? Yes, I have with Lolo (Koscielny).
"He would have liked to, he would quite like to. You will have to ask him the question."
Lloris would join an exclusive group of players including Sol Campbell, Emmanuel Adebayor and William Gallas in having played for both clubs.
Pep Guardiola issues a very blunt answer when quizzed by reporters on latest accusation levelled against Manchester City
'I think my opinion is more important than Roy Keane's. I know as a captain he does things sometimes with his arms, criticising his team-mates, but most of all it's a bit of frustration.' - Ruben Amorim hits back in Bruno Fernandes row
