Both officials will be forced out of their current seats by term limits next year.
Antonovich, 75, has represented the northern reaches of the county since 1980. His district, which includes the Antelope Valley, parts of the San Gabriel Valley, Pasadena and Glendale, overlaps with Liu's 25th state Senate district. He previously represented portions of the district in the state Assembly.
FOR THE RECORD: An earlier version of this post stated Antonovich's age as 76. He is 75.
Antonovich is one of two Republicans on the county board.
Registered Democrats outnumber Republicans in Liu's district -- 41% of registered voters are Democrats and 30% Republicans. The field shaping up for the 2016 race has been dominated by Democrats, including former Assemblyman Anthony Portantino and current Assemblyman Mike Gatto.
Antonovich said he believes a Republican can win the seat.
"The people are going to vote based on who represents them best, and I have an effective record representing the area," he said.
If he pursues the seat, Antonovich said he would focus on reining in state spending, creating jobs, expanding mental health services and improving public safety. He said that would include rolling back legislation that shifted responsibility for jailing and monitoring many nonviolent felons from the state to counties.
He said he expects to make a decision about the race in the next month.
Because of term limits approved by voters in 2002, the five-member county board is in the midst of a major membership shift for the first time in decades. Longtime Supervisors Zev Yaroslavsky and Gloria Molina were replaced last year by former state lawmaker Sheila Kuehl and former U.S. Secretary of Labor Hilda Solis.
Along with Antonovich, Supervisor Don Knabe will be forced out of office next year.
Follow Abby Sewell on Twitter at @sewella for more county news.