The two companies have made progress in negotiating terms and are nearing an agreement, according to Reuters, which cited unnamed people familiar with the situation.

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Sprint and T-Mobile US rallied in late stock trading Thursday on a report that the wireless carriers are aiming to complete a merger deal as early as next week.

The two companies have made progress in negotiating terms and are nearing an agreement, according to Reuters, which cited unnamed people familiar with the situation. The report sent Sprint shares up 7 percent in after-hours trading, while Bellevue-based T-Mobile climbed 3.9 percent.

Bloomberg News reported earlier this month that the two sides had restarted talks, five months after an earlier attempt fell apart. The previous discussions broke down after executives tussled over how control of the combined entity could be shared, people with knowledge of the talks said at the time.

The deliberations are further complicated because they involve overseas owners. Tokyo-based SoftBank Group owns almost 85 percent of Sprint, while Deutsche Telekom is the controlling owner of T-Mobile.

Representatives for the carriers didn’t immediately respond to requests for comment.

[Read more about T-Mobile, a cornerstone of the wireless industry in the Seattle area]