The Nordstrom family has offered to buy its namesake department store chain for $23 per share in cash with plans to take the retailer private for $3.8 billion.

Erik and Peter Nordstrom, the great grandsons of founder John Nordstrom, said they had been exploring ways to take the company private, according to a statement on Wednesday. The brothers formed a group with other family members and a Mexican department store chain El Puerto de Liverpool, which took a nearly 10 percent stake in the company two years ago.

The proposed transaction would be financed through a combination of equity and cash commitments by family members and Liverpool, as well as $250 million in new bank financing. Following the proposed transaction, the company would be 50.1 percent owned by the family and 49.9 percent by Liverpool, which operates 312 stores in Mexico.

The group said the offer represented a 34.8 percent premium over where the company’s shares were trading on March 18, when reports of discussions between the company and family surfaced. Nordstrom’s shares have risen 24 percent year to date through Tuesday’s close.

Nordstrom’s board of directors confirmed it had received the offer and that a special committee that included “independent and disinterested directors” would review the proposal.

Puerto de Liverpool said in a separate statement the proposal represents a new capital investment by Liverpool of at least $1.2 billion, which would be covered in part with its own resources and another part with financing.

By Max Zimmerman

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Nordstrom shares rose 6 percent on the news, giving the company a market value of about $3.3 billion.