* CEO praises Softbank's Son after T-Mobile-Sprint deal flops
* U.S. unit strong enough stand alone, cash flow abundant
* Telekom open to "consolidation and convergence" in U.S.
* Unlimited data plan lifts Germany mobile revenues (Updates with CEO comments, details, analyst, shares)
FRANKFURT, Nov 9 (Reuters) - Deutsche Telekom left the door open to a merger of its T-Mobile US business days after the collapse of a deal between its U.S. business and Sprint Corp.
Europe's largest telecoms company, which has a 64 percent stake in T-Mobile, also nudged up its annual core profit forecast on Thursday.
CEO Tim Hoettges said he regarded Japan's Masayoshi Son, the head of Sprint Corp's main owner Softbank Group, as one of the world's leading businessmen even after the two failed to agree terms.
"I have the highest respect for his life's work," Hoettges told reporters as Telekom announced a 3.3 percent gain in third-quarter core profits.
"I rule nothing out: you always meet twice in life."
Hoettges flew 50,000 km in seven days to try to save a deal to combine the third- and fourth-largest U.S. market players, only to call it off last weekend because it would not have added value.
Now, having spent billions at spectrum auctions in recent months, T-Mobile was generating enough cash to pay its own way.
"T-Mobile US is ideally positioned for an independent future," Hoettges said.
"That is not to say that the company is not open to considering consolidation and convergence options to further advance itself in the future."
Markets welcomed Telekom's results and the increase in forecast 2017 earnings before interest, tax, depreciation and amortisation (EBITDA) to between 22.4 and 22.5 billion euros ($26.0-$26.1 billion).
Earlier guidance was for EBITDA of 22.3 billion.
"The U.S. motoring ahead, Germany solid and the rest of Europe showing some signs of life," analyst Dhananjay Mirchandani of Bernstein Research said in a note. "A reason for cheer in an otherwise drab sector."
Telekom shares traded 0.2 percent higher at 1145 GMT.
Group net debt, at 52.6 billion euros, was up 8.6 percent year-on-year but down after peaking in the prior quarter.
That put Telekom's debt/EBITDA ratio - a measure of how well a company can manage its borrowing - at 2.3 times, within a comfort corridor of 2 to 2.5 times, said Chief Financial Officer Thomas Dannenfeldt.
In other highlights, mobile service revenues showed a 0.9 percent gain in Germany as Telekom offered unlimited data to customers under its Stream-On plan, copying the strategy behind T-Mobile's U.S. growth story.
Telekom also stepped up building out its high-speed glass-fibre broadband network, with Hoettges rebutting criticism that it was abusing its dominant market position by going slow, and arguing against tighter regulation.
Hoettges said Telekom had added 2.8 million fibre-optic lines in the last 12 months, and would connect another 3 million households by February of next year.
He also pushed back against suggestions that Germany's next government should sell Deutsche Telekom shares to fund the multi-billion broadband upgrade.
"It's not a money problem - at the moment it's a capacity problem," he said, adding that Telekom had drafted in companies from Spain, Morocco and Romania to do the job because Germany's civil engineering industry was running flat out.
On the downside, Deutsche Telekom booked a 1.2 billion euro impairment charge against goodwill at its T-Systems unit. Executives admitted they had been slow to anticipate a shift in IT services to a low-cost cloud subscription revenue model. ($1 = 0.8615 euros) (Editing by Keith Weir)