Reuters could not determine how much of a premium SoftBank may want Deutsche Telekom to pay for control of Sprint, which has a current market valuation of $36 billion.
T-Mobile's market value stands at $50 billion, which is about $20 billion higher than when it was last in merger talks with Sprint in 2014.
While Sprint's market value has changed little since then, T-Mobile has overtaken Sprint as the No. 3 wireless customer in terms of numbers of subscribers. T-Mobile said it had 71.5 million total customers while Sprint had 59.5 million at the end of 2016.
T-Mobile is now almost as big as Deutsche Telekom's German business. "We are not in the mood of selling the business," Hoettges told investors last November.
Under John Legere, its combative, T-shirt wearing chief executive, T-Mobile has rolled out unlimited data plans and international roaming packages. Combined with aggressive marketing, this has boosted T-Mobile customer base at the expense of its rivals.
While Sprint has also been growing its customer base as of late and improving its financials under CEO Marcelo Claure, it has done so primarily through heavy discounting. Despite new investment, the company's network is still viewed by many consumers as weaker than its rivals.
Barclays analysts wrote in a note in December that a merger of T-Mobile and Sprint could result in $25 billion to $30 billion in synergies but said, "it is not imminently clear to us that the various regulatory agencies would reverse course having already blessed the outcome of a four-player market."
The FCC and the U.S. Department of Justice sent strong messages in 2014 that they did not want Verizon, AT&T, Sprint and T-Mobile to merge among themselves.
Since then, AT&T acquired satellite television provider DirecTV and has signed an agreement to buy media giant Time Warner Inc, though that deal is still under regulatory review and has attracted criticism from U.S. President Donald Trump. Verizon has also been exploring other acquisitions.
Craig Moffett, an analyst at MoffettNathanson, said price wars between Sprint and T-Mobile have driven down overall wireless prices.
"Antitrust regulators could well argue that this is precisely the dynamic they would want to preserve," Moffett added.
Son has said he expects his company to benefit from Trump's promised deregulation of the U.S. economy. After meeting Trump in early December, Son pledged to invest $50 billion and create 50,000 jobs in the United States.
— CNBC contributed to this report.