Sprint Nextel currently owns 51.7 percent of Clearwire.
A deal struck in October has given Sprint Nextel, the third largest phone carrier in the country, the confidence and the cash to look for acquisitions that would help it to expand.
In October, Sprint Nextel sold a majority of its own stake to SoftBank of Japan for $20.1 billion, which greatly increased Sprint's purchasing power.
The offer to buy Clearwire would require SoftBank to sign off on the deal, The New York Times reported Thursday.
The offer from Sprint Nextel values Clearwire at $4 billion. It would give Spring Nextel a sizable portion of the wireless spectrum and the ability to speed up its pursuit of a next generation wireless network.