Second round bids for the NYSE-listed business, which has a current market valuation of about $1.16bn, are expected within the next two weeks according to the Wall Street Journal.
It cited people familiar with the matter, who said other private equity and industry players were also considering offers for parts of the company.
Reuters reported in July that Jones Group, which owns retail chains Nine West and Jones New York, had hired Citigroup to explore a potential sale.
In April KKR bought a 65 per cent stake in luxury apparel retailer SMCP from L Capital, with management holding the remaining share.
Financial details of the purchase were not disclosed, although reports at the time said the offer valued the brand at close to €650m.
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