In a tweet over the weekend, the agency shared that the deputies can help with the cleanup, despite Hollywood not being in their patrol area.
Villanueva compared the idea to last summer's effort in Venice, where the department cleared a major homeless encampment there after talking to various homeless individuals to gauge their interest in receiving government-provided housing.
That was another area within the jurisdiction of the LAPD, which has not publicly responded to the latest offer.
Villanueva's efforts in Venice drew criticism from some politicians and community organizations. A statement put out by a coalition of local advocacy groups said: "Time and time again, this approach has proven to fail in Los Angeles, and cause harm to people already dealing with crisis, trauma and the extreme lack of affordable housing across our region and especially on the Westside."
RELATED | LA County sheriff sends deputies to Venice, blames LA leadership for homeless issues
LA County sheriff sends deputies to Venice, blames LA leadership for homeless issues
But the sheriff said the homelessness crisis within Los Angeles city limits prompted him to take action, and accused Councilman Mike Bonin and Mayor Eric Garcetti of hampering the LAPD in its ability to do its job with regard to encampments.
"I'm not going to blame LAPD whatsoever," Villanueva said. "I think they can definitely do the job. They're more than capable, have good leadership. However, if they're hamstrung by politicians that don't want them to do their job, well, then they're left in a very, very bad situation."
City News Service, Inc. contributed to this report