The proposals were exchanged last week, said B.K. White, first vice president of USW Local 12-5, which represents 500 workers at the Richmond refinery who went on strike on March 21 after talks between the two sides failed.
A Chevron spokesperson was not available on Monday to discuss negotiations.
No meetings are planned in the coming week, White said.
Negotiators for USW 12-5 and Chevron last met on April 11 when Chevron put its proposal across the bargaining table. At the time, Chevron gave the union until Monday to reply, the company said in a statement issued on April 12.
Chevron has begun searching for temporary replacement staff to work with managers and supervisors who have been operating the 245,271 barrel-per-day (bpd) San Francisco Bay-area refinery since the strike began.
The strike began after the workers twice rejected contract proposals from Chevron.