Should Apple bite the bullet and join the big-screen smartphone camp or continue with its strategy of making phones that fit comfortably in the palm of your hand is the dilemma. But, according to a new report, Apple would do well to choose the first option.

As makers of Android-powered smartphones continue to increase the screen size of their handsets, the response from consumers has been remarkably positive, according to a new report from research firm Canalys, which said that more than a third of all smartphones shipped in the first quarter of 2014 sported displays that were 5 inches or larger, something that Apple Inc.’s (NASDAQ:AAPL) iPhone still lacks.

“Consumers now expect high-end devices to have large displays, and Apple’s absence in this market will clearly not last long,” Jessica Kwee, an analyst at Canalys, said in a statement. “It is notable that 5" and above displays featured on almost half (47%) of smart phones with an unlocked retail price of US$500 or more. Of the remaining 53% of high-end smart phones, 87% were iPhones."

According to the Canalys report, shipments of smartphones with screens equal to, or larger than, five inches grew 369 percent during the first quarter of this year, representing 34 percent of all smartphones shipped worldwide. Considering this significant shift in the smartphone market, rumors of Apple’s upcoming 4.7-inch and 5.5-inch iPhone 6 models now seem more plausible than ever before, according to Boy Genius Report, or BGR, a technology news website.

The BGR report said that consumers in the high-end smartphone segment prefer larger devices with powerful specifications, and in order to maintain its lead in the market, Apple needs to keep up with rival manufacturers such as Samsung Electronics Co. Ltd. (KRX:005935) and HTC Corp (TPE:2498), which have already begun offering smartphones with bigger displays.

According to ongoing rumors, Apple is expected to release two versions of the iPhone 6 -- a 4.7-inch model and a 5.5-inch model -- and the California tech giant could debut the 4.7-inch version of the iPhone 6 by August, and follow up with a bigger model in September, Reuters reported last week, citing Taiwan’s Economic Daily News.

If Apple’s 5.5-inch iPhone 6 becomes a reality, it would be a tough competitor for Samsung’s Galaxy S5 and Galaxy Note 3, which feature 5.1-inch and 5.7-inch screens, respectively.

Samsung, which currently remains the leading smartphone vendor with a 31 percent market share worldwide ahead of Apple at 16 percent, also leads the market segment for larger smartphones. According to Canalys, Samsung holds a 44 percent share among all devices with a screen size of five inches or more, while its share climbs to 53 percent in the 5.5-inch-plus category.

"Apple plainly needs a larger-screen smart phone to remain competitive, and it will look to address this in the coming months,” Kwee said.