Talks between both sides broke down late Tuesday night, meaning another strike is possible at any moment.
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On Sunday, concession workers held a one-day strike during the Bulls game ahead of the Big Ten men's basketball tournament.
The United Center is set to host the high-profile event, which will draw hoops fans from all over the country, starting Wednesday night.
Hundreds of union servers, bartenders, cooks and dishwashers are threatening to walk out.
The union said for more than two years, it's negotiated over healthcare and pension benefits with Compass/Levy, the UC's food and beverage provider.
RELATED: United Center concession workers strike days ahead of Big Ten tournament; demand better compensation
"Healthcare issues have been at the core for a very long time of a lot of very serious labor disputes," said Bob Bruno, professor of labor and employment relations at the University of Illinois.
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Late Tuesday night Compass/Levy released a statement, saying:
"At tonight's bargaining session, as we have now across 21 such sessions, we continued to improve our offer. We enhanced it this evening by proposing additional funding to lower the number of hours required to qualify for year-round health insurance, thus expanding the number of team members who will benefit. We will resume discussions at our next bargaining session scheduled for Saturday, March 11th.
"We are planning for food and beverage service at the Big Ten Tournament to continue as normal. In the event of a strike, menus will be adjusted to focus on fan favorites and top-selling items."
Compass/Levy also said at Tuesday night's bargaining session, they continued to improve their offer, but talks broke down.
In response, the union released a statement, saying "Compass/Levy failed to reach an agreement with UNITE HERE Local 1 and concessions workers at the United Center at last night's negotiations. Although contract talks with the company will continue on Saturday, March 11, a strike could begin at any moment, including during the Big Ten Tournament."
Tip-off for the first game is at 5:30 p.m. Wednesday, and another bargaining session is set for the weekend.