LightSquared would pay to use AT&T's fourth-generation network when it needs additional capacity, the news agency reported.
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AT&T and LightSquared did not immediately respond to requests seeking comment.
AT&T plans to invest $19 billion this year in its national wireless and wireline networks and other capital projects to enable 4G speeds across the country.
Reston, Virginia-based LightSquared is owned by two main investment funds of Falcone's $6 billion Harbinger Capital Partners hedge fund.
In March, LightSquared entered a roaming agreement with Leap Wireless International to help the low-cost carrier Leap access more network capacity from LightSquared.