RBI, which the person said had sharply reduced its exposure to the Signa group in recent years, declined to comment on Thursday.
The European Central Bank (ECB), which supervises the banks, declined to comment.
Raiffeisen Landesbank Niederoesterreich-Wien, Raiffeisen Landesbank Oberoesterreich and Erste Group are also among the banks with exposures to Signa, the person said.
The other two Austrian banks declined to comment.
A spokesperson for Austria's central bank said it had no concerns about the country's financial stability, when asked about Signa's financial position.
Persons:
UniCredit, Signa, Rene Benko, Fitch, Landesbank, Banks, Arndt Geiwitz, Francesco Canepa, Tom Sims, Elisa Martinuzzi, Alexander Smith
Organizations:
Signa Group, Chrysler, Raiffeisen Bank, Bank, European Central Bank, ECB, Reuters, Erste Group, Erste, Austria's National Bank, Market Authority, Thomson
Locations:
VIENNA, Banks, Austria, Bank Austria, Wien