Concerned about the cost to taxpayers, Villaraigosa asked his staffers Wednesday to come up with a plan to relocate the protesters or limit when they can be on the lawn.
The mayor said he wants a plan "that ensures the people's right to protest, a right to speak and to assemble, but also that we have time, place and manner, restrictions, requirements, that balance all of that."
Villaraigosa said the city was spending about $2,700 per day, mostly for General Services Department police officers to watch demonstrators. People also have been wearing out the lawn and inadvertently breaking sprinkler heads, he said.
Damage to the lawn could be as much as $400,000, according to the Department of Parks and Recreation.
The mayor suggested the protesters could be moved to city property near Temple and Main streets.
Villaraigosa said he respects the protesters' rights but they must in turn respect city laws. A spokesman for the city attorney said existing laws bar people from camping on city property after 10:30 p.m.
The mayor also said he has concerns about the camp becoming a health hazard.
"By saying it's dirty and it's a health hazard and we've got to close it down, it's a very convenient way of thwarting a movement that will put the people in positions of power and wealth at risk," said Bob Vanech, an Occupy LA protester.
City News Service contributed to this report.