Borders is writing its final chapter.

The nation’s second-largest book retailer, which employs more than 10,000 workers in nearly 400 stores, said yesterday it will ask a judge to approve a plan to liquidate after the chain failed to attract a white knight in a bankruptcy auction.

In New York City, Borders has six stores.

The 40-year-old bookseller, founded in Michigan by the brothers Tom and Louis Borders, fell victim to the Internet and the rise of electronic books — two areas where rivals Amazon.com and Barnes & Noble have been aggressive in recent years.

Just 20 years earlier, Borders and its large-format stores — which helped pioneer the practice of offering book browsers comfy chairs and selling them cups of coffee — had come under fire for pushing smaller mom-and-pop book shops out of business.

Last week, prospects dimmed for the book retailer’s survival when negotiations collapsed with private-equity investor Jahm Najafi, sources said.

“We were all working hard toward a different outcome,” Borders President Mike Edwards said. “But the head winds we have been facing for quite some time, including the rapidly changing book industry, (electronic-book) revolution and turbulent economy, have brought us to where we are now.”

After filing for Chapter 11 in February, Borders struggled to persuade publishers to ship books to its stores — after they had grown skittish about the retailer’s tight liquidity.

Borders has asked a judge to approve on Thursday a bid submitted by a team of liquidators led by Gordon Brothers and Hilco Merchant resources.

Going-out-of-business sales could begin as soon as Friday, with the chain closing its doors for good by the end of September, officials said.