"There are a bunch of committees" that have to reach agreement before a deal can be signed, said the person, who requested anonymity because the talks are private.
Negotiators were to return to the bargaining table Sunday afternoon after breaking Saturday night, the person said.
Chrysler spokeswoman Michele Tinson said Sunday that the two sides were making progress.
"We remain optimistic," she said.
A message was left for UAW spokesman Roger Kerson.
General Motors Corp. already has reached a tentative agreement with the UAW that GM workers are now voting on. The union has not formally picked the second company it will negotiate with, but talks with Chrysler have intensified in recent days.
The UAW's contracts with Chrysler, Ford Motor Co. and GM were originally set to expire Sept. 14. The UAW selected GM as the lead company and strike target and reached a tentative agreement Sept. 26 after a two-day walkout.
The deal won't go into effect until it is ratified by GM workers, a process expected to end Wednesday. Chrysler and Ford have been extending their contracts indefinitely.
The UAW typically reaches an agreement with one automaker and then tries to get the others to match the terms. But industry analysts have said that the GM deal probably won't fit Chrysler and Ford exactly and changes are likely.
The UAW represents about 49,000 hourly workers at Chrysler, making it the smallest of the domestic automakers. The company also has around 78,000 retirees and surviving spouses represented by the UAW.
Chrysler recently became a private company, which could be a factor in the talks. Private equity firm Cerberus Capital Management LP bought a majority share of Chrysler in August from DaimlerChrysler AG. As a private company, Chrysler no longer has shares and is not required to file earnings reports.
Chrysler pays its workers an average of $75.86 (53.66 EUR) per hour in wages, pension and health care costs, the highest among the Detroit automakers.