The Galaxy have already knocked back a £5 million offer for Beckham but if a deal cannot be done by Friday 13 February, he will have to return to the MLS in March.
"There is no reason why this should drag on," MLS commissioner Don Garber said.
"They either want to do it or don't want to do it.
"This Friday we need to know if they want to buy David Beckham or not.
"What they need to realise is that we are getting very close to the start of our season.
"We have to figure out what plans we need to make and if David Beckham is going to be a part of those plans."