There already appears to be bad blood between the rival French strikers – with the pair potentially fighting for a single front man position.
Giroud could be searching for an Emirates exit – with Everton and Borussia Dortmund among the interested parties – after Lacazette was brought in for a club record £52m earlier this month.
But the attacker, who netted 18 times for the Gunners last season, will not leave without proving his worth in Arsene Wenger’s side.
Giroud said about his future last last week: “Honestly, I don’t know at the moment but I’m still an Arsenal player so I try to be professional like I always have done and prepare well for next season.
“Obviously there will be more competition, even more than last year, but it’s always nice for a striker to feel the pressure. I always deal with it.
“This one, I don’t know. This year I don’t know about my future so I can’t tell you more. I’m focused on pre-season.”
Giroud slotted in a tap-in in the 33rd minute of their clash with Western Sydney Wanderers – as they ended their pre-season tour of Australia.
In his celebration he seemed to blank Lacazette – as the new recruit from Lyon stuck out his hand to offer a congratulatory high-five.
Later, Giroud failed to pass to Lacazette.
Gunners fans noticed the lack of interaction and took to social media to express their opinions.