Tuesday, Office Depot surged 9.4 percent, to close at $5.02. OfficeMax rose 21 percent to $13.
On Feb. 15, Office Depot closed at $4.59, down from a peak of $44.46 in May 2006. That gave the company a stock market value of $1.31 billion, more than OfficeMax's value of $932.5 million based on last week's $10.75 closing price.
Julie Treon, a spokeswoman for OfficeMax, would not confirm merger talks.
"There have been rumors for a while about consolidation in the marketplace," she said by phone. "It's also been our policy not to comment on market rumors or speculation."
Brian Levine, a spokesman for Office Depot, declined to comment in an e-mail.
The Wall Street Journal reported the talks Monday on its website.
A combined company might generate as much as $580 million in cost savings, Daniel Binder, an analyst for Jefferies & Co. in New York, wrote in a note to clients. Both chains have been closing locations, and that trend would accelerate with a merger as about 50 percent of their store territories overlap, he said.
A combined OfficeMax and Office Depot might close or sell as many as 600 locations, giving Staples an opportunity to increase sales in those areas, Gary Balter, an analyst for Credit Suisse Group AG in New York, wrote Tuesday in a note to clients.
In statements earlier this month, Office Depot said it had about 1,675 global locations, and OfficeMax said it had about 900 stores in the U.S. and Mexico.
Staples had 2,295 stores worldwide as of Jan. 28, 2012. Its stock rose 13. percent Tuesday, closing at $14.65.
Any deal struck may be challenged by the Federal Trade Commission, said David Balto, an antitrust attorney in Washington who worked on the FTC's lawsuit that stopped Staples from acquiring Office Depot in 1997.