The former Chelsea and Arsenal attacker has entered the final six months of his contract at San Siro, leaving him free to enter pre-contract discussions with foreign clubs.
Giroud's goalscoring powers have not waned despite his advancing years, as he has found the back of the net 14 times in 36 matches across all tournaments this season, in addition to chalking up nine assists.
However, France's all-time leading male goalscorer will celebrate his 38th birthday in September, and the Rossoneri have not been expected to sanction a new contract for Giroud as they plan for the future.
The World Cup winner seemingly has no intention of hanging up his boots just yet, though, and a move to North America has been touted should he call time on his career in European football.
A proposed switch to the United States is now said to be inching ever closer, as journalist Fabrizio Romano reports that Los Angeles FC and Giroud have reached a verbal pact over a transfer, five months on from when the Black and Gold first registered their interest.
Giroud is expected to sign a contract until December 2025, which would keep him in MLS until after he turns 39, and a move should go through without any hitches once all the relevant documents are signed.
Which veteran players will Olivier Giroud join in MLS?
While a plethora of soon-to-be ex-players - and some athletes at the peak of their powers - have been seduced by the riches of Saudi Arabia, plenty more have opted to try their hand in MLS, most notably eight-time Ballon d'Or winner Lionel Messi.
The former Barcelona man headlines a quarter of ex-Blaugrana stalwarts on the books at Inter Miami, who also have Luis Suarez, Jordi Alba and Sergio Busquets in their ranks - boasting a combined age of 107.
Giroud's proposed move to MLS will also see the experienced Frenchman reunite with another 2018 World Cup winner in Hugo Lloris, now guarding the goal for Los Angeles FC, and he is the seventh-oldest player to make an appearance in the division this term.
Coming in at 37 years and two months old, Lloris is just two years younger than the oldest player in the current MLS season - 39-year-old Atlanta United goalkeeper Brad Guzan, once of Aston Villa, Hull City and Middlesbrough and still going strong six months before his 40th birthday.
Martin Caceres - a Champions League winner with Barcelona - is plying his trade with Los Angeles Galaxy, while Maya Yoshida, Teemu Pukki, Christian Benteke, Lorenzo Insigne, Ashley Westwood and Asier Illarramendi have all crossed the Atlantic to represent MLS clubs too.