In order to meet the demand, Pegatron has started building a new plant at Kunshan, a satellite city near Shanghai where all its iPhones are assembled, the Liberty Times said without identifying its source.
The paper said the Kunshan plant is scheduled to become operational in the middle of the year and start mass production late this year, when Apple is expected to roll out its iPhone 6.
(Also see: iPhone 6 to come with larger screen, due May 2014: Report)
It said Pegatron expects its revenue to rise to Tw$950 billion ($31.5 billion) this year, from Tw$882 billion the previous year, thanks largely to Apple orders.
Pegatron declined to comment on the report.
A company official told AFP the new plant at Kunshan was intended to meet demand for the next two to three years, but did not elaborate.
The report came amid growing speculation that Apple may offer a smartphone with a bigger screen compared to the four-inch screen of existing models.
(Also see: iPhone 6 to feature a 4.8-inch screen: Report)
Samsung Galaxy S4, an improved version of the South Korean company's popular predecessor the Galaxy S3, boasts a five-inch screen.
Such handsets are often referred to as "phablets" because their size sits in between a phone and a tablet.
Pegatron produces consumer electronics such as game consoles, television sets and computers for Sony, Toshiba and other brand-name vendors, as well as assembling products for Apple.
Since 2012 Apple has reportedly been shifting orders from another Taiwanese assembler Foxconn to Pegatron for the iPad mini and the iPhone 5c.
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