Shares of Staples and Office Depot are soaring in Tuesday premarket trading on speculation that the office supply companies are discussing a potential combination.

The Wall Street Journal reported that Staples and Office Depot are in advanced talks about a possible deal, citing people it did not identify who it said are familiar with the matter. The report said that the price and structure of the proposed transaction is not known, and that there's no guarantee a deal will be reached.

Staples has a market capitalization of approximately $11 billion, while Office Depot — which combined with OfficeMax in a $1.2 billion deal in November 2013 — has a market capitalization of about $4 billion.

Last month activist hedge fund Starboard Value LP urged Staples to combine with Office Depot. In a letter sent to Staples CEO Ronald Sargent, Starboard recommended the Framingham, Massachusetts-based company immediately hire an investment bank and legal advisers to help the board evaluate, structure and execute a transaction with Office Depot.

Starboard disclosed in a regulatory filing in December that it purchased a 5.1 percent stake in Staples and boosted its stake in Office Depot. New York-based Starboard has a history of buying stakes in companies and shaking them up.

Representatives for Staples and Office Depot, which is based in Boca Raton, Florida, did not immediately respond to emails seeking comment.

Office Depot Inc.'s stock rose 15.6 percent to $8.82 in premarket trading more than two hours ahead of the market open while shares of Staples Inc. climbed 11.5 percent to $19.14.