CNBC reported that the pair have begun active discussions.
"While the talks continue with vigor and advisors have been engaged on all sides, people close to the situation stress they are still weeks away from finalizing a deal and believe the chances of reaching that deal are not assured," it said.
The talk of the two merging is nothing new.
Both firms and their parents, Deutsche Telecom and Softbank, have been in talks before about a stock-for-stock merger, which would enjoy considerable cost synergies.
Deutsche Telecom, the T-Mobile parent, would become the majority owner.
Sprint Corp shares added over 8% in early deals to US$ 8.34. T-Mobile US inc (NASDAQ:TMUS) added 3.82%. In Frankfurt, Deutsche Telekom AG shares added 2.88% to €15.54.
The last time the two companies held talks earlier this year, Softbank's Masayoshi Son indicated a willingness to sell sprint to T mobile.
*T-Mobile, SPRINT ARE SAID IN ACTIVE TALKS ABOUT MERGER: CNBC— *Walter Bloomberg (@DeItaOne) 19 September 2017