According to LACMA, the goal is to cut costs by combining the operations and infrastructure of the two museums but maintain their independence.
The MOCA Board of Trustees, which met Tuesday and will reconvene Thursday, released a statement saying it was grateful for the agency's generosity, and that it was considering options for the museum's long-term health.
The merger would involve the volunteer, not-for-profit boards and private funding sources and would not involve financial support from the county, according to LACMA.
"A merger of board leadership, including some of MOCA's founders and artists, could provide a unique platform for the preservation and growth of MOCA's programs, under MOCA's name, with expanded facilities, in combination with a strong director and management team already in place," said Andrew Gordon, chair of the board of LACMA.
Under the proposal, MOCA's collection and programs would be housed at the Geffen Contemporary at MOCA and the Broad Contemporary Art Museum and Lynda and Stewart Resnick Exhibition Pavilion at LACMA.
Other programs would be planned for the Grand Avenue development.
MOCA receives only minimal government funding. Its annual budget has grown to exceed $20 million, but it relies on donors to pay about 80 percent of its expenses.
As tough economic times have hit, gifts have dried up, driving the museum to borrow from its endowment and depressing the overall value of that fund.