Leonard Green, based in Los Angeles, would provide the Nordstrom family members with about $1 billion in equity to help fund the deal, CNBC reported Tuesday.
In early June the company disclosed that family members were considering a bid to take the company private.
The Nordstrom family members — company co-Presidents Blake Nordstrom, Peter Nordstrom and Erik Nordstrom; President of Stores James Nordstrom; Chairman Emeritus Bruce Nordstrom; and Anne Gittinger, granddaughter of Nordstrom co-founder John Nordstrom — had not made any proposal, the company said then.
The group owns 51.8 million shares, representing about 31.2% of the company's outstanding stock, it said in a June regulatory filing.
A spokeswoman for the family group declined to comment on the report, as did the company.
The report late Tuesday followed weeks without news of progress on an offer. Nordstrom Inc. shares climbed 6% to $47.74 on Wednesday, up from the $47.16 price immediately after the proposed buyout was disclosed more than three months ago.
After the disclosure months ago, the company said its board of directors formed a special committee of its independent members to represent the best interests of other shareholders in considering any possible transaction.
That committee could also solicit proposals from other outside entities, though the Nordstrom family indicated in the regulatory filing that it had "no interest in a sale of their shares" to a third party or voting for an alternative transaction.
Leonard Green has invested in retail companies such as BJ's Wholesale Club and Joann Stores, the fabric and craft chain.
Despite Nordstrom's record as one of the better-performing department store merchants, financiers are thought to be reluctant to wade into a sector that has seen plenty of recent failures.
A group of analysts led by Michael Binetti at UBS Investment Bank estimated in June that the family would need to raise $4 billion to $4.5 billion in outside capital, assuming a final stock price of $50 a share and backers from the private equity world contributing $1.5 billion of the total buyout.
"We're cautious about a department store's ability to secure a bid of this magnitude given the structural headwinds facing the sector today," the UBS analysts wrote in a research note June 8. "Five years ago, Best Buy went down a similar path looking for $2.5-$3.0B and was unable to secure the full funding."