Shares of the U.S. electronics retailer rose as much as 10 percent to its highest level since September 2007.
Investment bankers have already begun pitching their private equity clients about a leveraged buyout of RadioShack, informing them of the retailer's willingness to sell, the newspaper said.
Another option for RadioShack would be a merger with bigger rival Best Buy Co Inc
Both RadioShack and Best Buy said in separate emails that their policy was not to comment on market rumors.
It is still early in the process and any sale efforts would not begin for weeks or even months, a source told the paper.
RadioShack shares have risen in the past on takeover speculation, but some analysts were skeptical about its chances of being bought because of weakness in the chain's accessory business.
RadioShack shares have nearly tripled over the last year as it repositioned itself as a hub for mobile phones and related services. Sales of mobile phones and related equipment were strong in the fourth quarter, but demand was weak for TV converter boxes, video game systems and batteries.
RadioShack shares were up $1.66 at $23.46 after touching an intraday high of $23.91. Best Buy shares rose 1 percent, or 42 cents, to $43.08.
The report also prompted bullish option activity.
On Friday, the most popular option gave investors the right to buy the firm's shares at $25 apiece by mid-April.
The action appears to be call buyers, which is rational if the market now expects increased odds for the stock to rally, said Jud Pyle, chief investment strategist at Options News Network, a division of option market making firm PEAK6 Investments in Chicago.
In all, traders exchanged about 14,000 call options, nearly double its recent average daily volume compared with 3,899 puts in RadioShack in the afternoon session, according to option analytics firm Trade Alert.
(Reporting by Sakthi Prasad in Bangalore, Doris Frankel in Chicago and Dhanya Skariachan in New York; Editing by Derek Caney)