EE beat off competition from Argos and Talk Talk, and the deal is now just subject to approval from administrators.
Citing a person close to the talks, the FT says a deal has been agreed for Life Mobile, the mobile arm of Phones 4U, which has around 85,000 subscribers.
EE, along with Vodafone, withdrew its products from Phones 4U stores, precipitating the company's fall into administration.
Since the company entered administration, EE and Vodafone have bought various elements, adding them to their own retail chains. They kept a few hundred stores open, saving a significant number of jobs.