The current three-year contract expires on July 1, and slowdowns at ports such as the busy Port of Los Angeles are possible even before the deadline hits.
Employers want to add technology to make operations more efficient, but longshoremen are afraid this would mean loss of jobs.
Teamsters President James Hoffa has been asked to attend the negotiations, and has said he will do so as his schedule permits.
Shippers have already begun to make preparations for a possible strike or lockout, according to the Journal of Commerce. Some are shipping cargo early or are looking for alternative routes.
During previous contract negotiations in 1999 and 1996, longshoremen staged slowdowns to pressure employers during negotiations.