A search for the captain of the Paloma ended at about noon. Coast Guard officials said the captain, believed to be Timothy Lybrand, might have swam ashore.
Debris from the vessel washed ashore and diesel fuel and oil leaked on the beach.
The Paloma is registered to Lybrand in Santa Cruz in Monterey Bay south of San Francisco.
Renee Martin, a spokeswoman for the Port of San Francisco, said Lybrand usually fished alone for salmon along the coast. She said on Monday he left San Francisco Bay at 2:30 a.m.
A short time later, Lybrand got in touch with the Sunrise, a nearby vessel, which sent out a radio call for help. Lybrand is believed to have then tried to swim about 25 feet to shore.
"The possibility that he could have swam in is relatively high," Coast Guard Lt. Sean Kelly said.
The vessel grounded at the north end of Ocean Beach, which runs along the San Francisco oceanfront and is part of the Golden Gate National Recreation Area. It was found empty at 3:30 p.m.