Sprint stock gained 7.9 percent on heavy volume on the New York Stock Exchange, while Nextel, trading at four times its normal volume on the Nasdaq Stock Market, rose 6.6 percent.
Both companies, frequently mentioned as suitable merger partners, declined comment on the reports.
The Wall Street Journal reported on the prospect of a merger in yesterday's editions. Later in the day, the Journal reported on its website that negotiations were underway.
Sprint is the nation's third-largest cellular company in terms of subscribers, as well as a major provider of local and long-distance telephone service for homes and businesses.
Nextel -- the fifth-largest wireless company and the only national cellular provider that's an independent entity -- is especially popular among spread-out groups of workers who use the walkie-talkie feature on Nextel's phones to keep in constant contact.
A merger would create a company with more than 38 million wire-less subscribers, making it a more potent rival to Cingular Wireless and Verizon Wireless by allowing the combined company to pool resources and cut costs.
It also would give Sprint a better presence in business markets while providing more bandwidth and services for Nextel, which does not have a high-speed wireless Internet offering like Sprint.
Cingular, a joint venture between SBC Communications Inc. and BellSouth Corp., recently completed its acquisition of AT&T Wireless to become the nation's biggest cell company with 47.3 million customers. Verizon Wireless, a partnership between Verizon Communications Inc. and Vodafone Group PLC, is next with about 42 million subscribers.