The 34-year-old is set to leave Chelsea this season, either in January or at the end of his contract next summer.
Inter Milan are still keen on the veteran Frenchman, but Beckham wants him in Major League Soccer.
It is the same building in which Lionel Messi owns an apartment that takes up an entire floor of the building.
Alternatively, Beckham has another option for Giroud in a spectacular mansion in Sunny Isles Beach.
But it remains to be seen if he wants to leave Europe ahead of next summer's European Championships.