The two were previously discussing a merger as recently as February, before talks broke off.
T-Mobile jumped as high as 4.17% in trading Tuesday morning, while Softbank-controlled Sprint spiked 7.83%.
A merger of the two would be a stock-for-stock deal, with T-Mobile controlling shareholder Deutsche Telecom coming out with the most shares, CNBC says.
Talks between Sprint and other companies about a merger have been intermittent for years, with no success. Reuters reported in June that the carrier was in talks with cable companies Charter Communications and Comcast about a possible partnership, but the those were put on hold when SoftBank entered into exclusive negotiations with Charter and Comcast.
Three years ago, Sprint ended talks to acquire T-Mobile after antitrust regulators voiced opposition.
T-Mobile and Sprint are currently the third- and fourth-largest U.S. wireless were providers.
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