"There's no reason why this should drag on," said Garber. "They either want to do it or don't want to do it."
Galaxy boss Bruce Arena believes Beckham will honour his contract in the US if the two clubs cannot agree on a permanent switch.
"When Milan give us what they feels is their best offer, we'll examine it and make a decision whether it's in the best interests of our club or not," Arena told BBC Radio 5 Live.
"If David Beckham returns, he is a good professional and he's going to play, and play well.
"Beckham understands what a contract means. He will honour his contract, whether it's with LA Galaxy or AC Milan."
But Beckham, who equalled Bobby Moore's England record of 108 caps for an outfield player when he featured against Spain on Wednesday, has reaffirmed his desire to stay in Italy.
"I am still hopeful," said Beckham ahead of Sunday's top-of-the-table derby against Inter Milan.
"It is something I want to happen, but we have to wait and see. We want it sorted out as quick as possible."
And Milan skipper Paolo Maldini has expressed his wish to see Beckham sign a permanent deal at the Italian club.
"I don't know how his contractual problems will be resolved but if they are resolved we'll be very happy to have him until the end of the season and next year too, being as that is what he wants," said Maldini.
"When two people meet and they are happy I think there should be a marriage."
The Milan derby is live on BBC Three at 1900 GMT on Sunday, with live text commentary on the BBC Sport website too.
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