A mock-up of the iPhone with 4.94-inch screen. The iPhone with a bigger screen size is expected to compete against Samsung’s 5.7-inch Galaxy Note 3 in the “phablet” category. Marco Arment

The 2014 model of Apple’s (NASDAQ:AAPL) iPhone, dubbed the “iPhone 6,” may sport a radically different design as the company is rumored to be working on future iPhone models with a much bigger and curved display.

Citing “a person familiar with the plans,” Bloomberg reported on Monday that Apple may release two new models of the iPhone in the third quarter of 2014 with both versions featuring “larger displays with glass that curves downward at the edges.”

The two new iPhone models would feature screen sizes of 4.7 inches and 5.5 inches, according to the report, and the larger screen sizes are expected to help Apple position its flagship smartphone strongly against the 5.7-inch Galaxy Note 3, which Samsung (KRX:005935) launched in September. Samsung also launched the Galaxy Round last month, the company’s first curved-screen smartphone.

“Screen size is one of the things where Apple has to catch up to the Android camp,” Dennis Chan, an analyst at Yuanta Financial Holding Co. in Taipei, told Bloomberg. “Innovation in components has been a key for Apple since the first iPhone came out.”

In addition to the bigger iPhones, the report also claimed that future iPhones may incorporate more advanced touch sensors that would be capable of detecting heavy and light touches on the curved screen. However, such pressure-sensitive technology is “unlikely to be ready for the next iPhone release and is instead planned for a later model,” the report said.

Sunday’s report supports some earlier rumors suggesting that the upcoming iPhone 6 could have a larger screen. Reuters had reported, in June, that the iPhone's 2014 model may come with at least two bigger screen sizes -- 4.7-inch and 5.7-inch -- as Apple is considering expanding its flagship smartphone range.

The Wall Street Journal reported in September that Apple was considering exploring the so-called “phablet” segment by testing iPhones with screen sizes ranging from 4.8 inches to 6 inches.

Analyst Ming-Chi Kuo of KGI Securities also said that Apple may introduce a bigger iPhone in 2014. However, he expected the company to release a handset with a screen sized between 4.5 inches and 5 inches, unlike the latest rumor that suggests a display as large as 5.5-inches.

In October, Korea’s ETNews reported that the iPhone 6 in 2014 may feature a bigger screen size of up to 5 inches. According to the report, a similar design alteration could apply to the iPad as well, which could feature a bigger 12.9-inch screen.