"Purely theoretically, we can see several advantages to consolidation and convergence," Deutsche Telekom Chief Executive Tim Hoettges told reporters after its first-quarter results.
"The strong position we have established for ourselves gives us the time and space to evaluate all options together with colleagues in the U.S.," Hoettges said.
T-Mobile US, which is 64 percent controlled by Deutsche Telekom, was the main driver behind the German telecoms operator's better than expected 7.5 percent rise in core profit.
Last month, T-Mobile US reported a 2.7 percent rise in post-paid customers to 35.3 million, continuing the steady increase in its subscriber base over the past four years.
Verizon, however, lost 307,000 retail post-paid customers or those who pay a monthly bill, in the first three months of 2017, the first quarter it has ever lost subscribers. AT&T lost 191,000 post-paid subscribers.
Unlimited data plans are among the latest incentives, one of many T-Mobile US initiatives shaking up the U.S. wireless market. In February, Verizon followed suit to offer an unlimited data plan for the first time in over five years.
"T-Mobile US continues to grow at breakneck speed," wrote Bernstein analyst Dhananjay Mirchandani, reiterating a "market perform" rating. "Leading indicators remain strong."