Giroud found the net as Milan claimed a 3-2 victory over rival Inter on Sunday (AEST), his 13th goal in just 25 Serie A starts for the Rossoneri.
The 35-year-old signed an initial two-year contract when he made the move to Italy in July 2021, but is keen to play on beyond the end of this season and has been inspired by the hunger of his fellow Milan striker Ibrahimovic.
Giroud said: "I still have the motivation and determination. I think the state of mind is important at my age.
"I would like to continue, but only if my body will allow me.
"I was discussing it with Ibra. For him it is the same, Zlatan is still hungry."
Ibrahimovic, 40, scored eight times as Milan ended an 11-year wait for the Scudetto last season, having also plundered 14 goals in 29 appearances when the Rossoneri were last crowned champions of Italy in 2010-11.
While Milan's Scudetto triumph represented Giroud's first league title since winning Ligue 1 with Montpellier in 2011-12, his trophy haul includes a 2018 World Cup win with France.
Giroud, who is just three goals short of matching Thierry Henry as the most prolific player in Les Bleus' history, has scored two international goals in 2022, and is keen to feature at his third World Cup later this year.
"I don't know anything honestly, also because I'm not the coach. But obviously it must be a goal," he said.
"With my history with France, having the chance to play a third World Cup is a chance. I think, if that was not a goal, it would be nonsense.
"The number one goal is daily life with Milan, France is still a bonus.
"If I am world champion for the second time, I will have to do something a little crazy, [like] shave my beard!"
Meanwhile, Giroud is set to be reunited with one of his former clubs next month, with Milan travelling to Chelsea in the Champions League on October 5.
The striker retains much affection for the club and believes he will receive a positive reception at Stamford Bridge, adding: "I hope for a warm welcome from Chelsea in London. I left the Blues on good terms, like all my other clubs.
"Returning to play with Milan at Stamford Bridge is great. I think it will be a good moment."