Although a listing would drag out the sale process for VEBA, it will be hoping to get a better price from investors or to force Fiat to increase its offer.
Meanwhile Fiat, which already owns 58.5 percent of Chrysler, will be hoping the stock market's valuation of the U.S. carmaker will show its existing offer is VEBA's best option.
"It's in the interest of both parties, but of Fiat in particular, to reach an agreement before a Chrysler IPO," said ICBPI analyst Luca Arena.
At 1040 GMT, Fiat shares were down 0.3 percent at 6.13 euros, extending losses on Friday after Fiat chief executive Sergio Marchionne said he was not getting any closer to striking a deal with VEBA.
Marchionne, who is also the chief executive of Chrysler, was quoted by the Financial Times newspaper on Monday as saying the U.S. carmaker was planning to file documents with regulators for the stock market listing this week—earlier than expected.
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"We need to go trough this process of determining value," he said. "(VEBA) have been very clear that they are not long-term holders of the assets. They want to monetise so we need to find a way that ... does not create what I consider to be exceptionally high or abnormal expectations of value."
Marchionne said on Friday any listing could take place in the last quarter of this year but was more likely to happen in early 2014, and could delay his plans for a full merger of the two groups.
People familiar with the matter have told Reuters that VEBA is seeking more than $5 billion for its stake, which it obtained as part of Chrysler's 2009 bailout.
UBS analysts estimate the stake is worth about $4 billion.
VEBA can sell a stake of up to around 25 percent of Chrysler in a stock market listing. The rest is locked as part of an agreement that allows Fiat to exercise options to gradually buy portions of the VEBA holding.