Sycamore has made an offer, while Chico's continues to be in talks with other bidders, Bloomberg reported, citing people familiar with the matter.
Chico's shares rose nearly 12 percent to $16.90 in extended trading on Friday.
The company has hired investment bank Peter J. Solomon to explore options available to it, Bloomberg said.
Chico's and Peter J. Solomon were not immediately available for comment. Sycamore declined comment.
Reuters reported in February that Sycamore was in talks to buy Chico's and was securing debt financing for a deal that could reach $3 billion.
Chico's, which caters to women over the age of 40 years, has been struggling to boost sales in the face of increased competition from fast-fashion retailers such as H&M Hennes & Mauritz AB.
The company said in August it would exit its Boston Proper business as it focuses on its Chico's brand business.
Up to Friday's close of $15.12, Chico's stock had fallen nearly 7 percent this year.