Juan Garzon/CNET

It's the eternal question for Google: Will the search giant come out with its own version of the iPhone?

Apple turned itself into one of the most powerful companies in the world on the strength of the little rectangular device: a premium, flagship phone with both hardware and software designed in-house. The company sold so many iPhones that it turned the phrase "Designed by Apple in California" into an iconic stamp, which the company made into a warm, fuzzy commercial.

It's the kind of gadget success Google would kill for. So the question keeps popping up. And it popped up again Monday after The Telegraph reported, according to anonymous sources, that Google would make its own branded phone and release it by the end of the year.

A Google spokeswoman said the company does not comment on "rumor or speculation."

The move would be a huge step for Google. Right now, the closest things to official Google phones are devices from the company's Nexus program. For those gadgets, Google decides exactly how the software will look and has a hand in designing the hardware. Still, it leaves the actual hardware making to a handful of partners, from LG to Huawei to HTC.

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That's one reason Google might want to keep its plans close to the vest -- to not freak out those companies that depend so much on the Nexus program to give their products a boost. Google, for its part, said it's still committed to Nexus.

Google has repeatedly downplayed the idea of the company making its own phone. When asked specifically at Recode's Code conference earlier this month, Google CEO Sundar Pichai's answer was "no." "Our plan is still to work with OEMs [or hardware manufacturers] to make phones," he said.

Hiroshi Lockheimer, chief of Google's Android mobile software, had a similar answer. In a profile of Lockheimer earlier this year, CNET asked about Google making its own phone. Lockheimer said the company chooses to make devices that consumers can't really get elsewhere. He pointed to Google's Chromecast streaming stick, which was novel when the company first started making them in 2013. But there's no shortage of phones on the market. "Phones are good," he said.

Still, Google wouldn't be faulted if it wanted to tighten the screws on Android. It's the most popular mobile software in the world, powering four out of every five smartphones on the planet. But one common criticism is something called "fragmentation." That refers to Google not being able to maintain a consistent Android experience from phone to phone because so many different hardware makers and wireless carriers are involved, and each of them add their own flourishes to the software.

If Google made its own phone -- and put the full strength of the Google brand behind it -- the company could better control the software.

There is one exception to Google building its own phone hardware. Project Ara is the company's attempt to build modular phones, with interchangeable parts you could swap out like Legos. Those phones will go on sale to consumers next year.

But that's a far cry from Google's version of an iPhone -- so far.