Glory chief executive Paul Kelly said it could cost up to $2 million dollars to bring the team to Perth, meaning ticket prices would likely start at around $50.
The game would be played at the 42,000-capacity Patersons Stadium should the Galaxy decide on Perth.
"The club doesn't want to lose money," Kelly said on Thursday.
"Beckham in itself is a worldwide brand and ... it was only last week he was on the front of Women's Day, so I think he'd have that appeal for anyone in general, not just football supporters.
"To put a percentage on (our chances of luring the team here), given we've had one or two conversations on it, 60-70 per cent at this stage.
"I'm quietly confident that if I can get everything in the mix we can put a good proposal forward and that may bring LA Galaxy to Perth."
Kelly said it would be a major coup if Perth was successful in their bid.
"They're a quality team in the MLS. Beckham's not the only player (of interest)," Kelly said.
"They've just signed Robbie Keane for two million dollars and a three-year contract, so he himself will have some interest."