The Korea Economic Daily claims that there has been huge demand for the Galaxy S3 since it was unveiled in London earlier in the month.
Thanks to the popularity of its Galaxy smartphones, Samsung was able to unseat Apple as the world's biggest maker of smartphones in the first quarter.
The latest version of the Android-powered Galaxy S, featuring a 4.8-inch screen and fast quad-core processor, will go on sale in Germany on May 29, before expanding to several other countries a day later.
Citing an unidentified Samsung official, the Korea Economic Daily said that the company's smartphone factory in South Korea was working at its full capacity of 5m units per month to meet the expected demand.
Samsung declined to comment on the report, but it did say late last month that the Galaxy S3 would "substantially contribute" to its second-quarter earnings.
Other reports have suggested that Apple will look to increase the screen size of the next generation of its iPhone in response to the success of Samsung smartphones.
The new iPhone is expected to launch later in the year and mark the biggest redesign in several years for Apple's popular phone handset, as the US firm looks to take back its smartphone crown from Samsung.