The Wall Street Journal cites "people briefed on the matter" as saying that a cheaper version of the iPhone, often dubbed the "iPhone Mini", could launch later this year.
Apple is known to have explored the launch of a less expensive iPhone for several years, but the Journal's sources say that the plans are now "progressing".
They claim that the iPhone Mini could resemble a standard iPhone in design, but with a different and less expensive body.
For example, Apple could lower production costs for the device by using a different shell, such as polycarbonate plastic rather than the aluminium body in the iPhone 5.
Other parts could remain the same, or be "recycled from older iPhone models", said the Journal's sources.
Apple could still drop the iPhone Mini plan, the sources added. A spokesman for the California-based firm declined to comment on the report.
Last week, Strategy Analytics executive director Neil Mawston told Reuters that his agency believes the so-called iPhone Mini will arrive next year.
"We think Apple will have to launch an 'iPhone Mini' at some point over the next three years to address the hundreds of millions of pre-paid users worldwide that cannot afford the current iPhone," he said in an email interview.
"The iPhone 5 is growing fast and profitably right now, so there is little incentive for Apple to launch an 'iPhone Mini' this year. We expect the iPhone Mini to be more likely next year, in 2014 when... Apple will be forced to discover fresh growth streams."
Apple is under big pressure to make the iPhone more affordable. Google's Android has become the dominant mobile operating system in the world as it powers a broad range of mobile phones of differing specifications and price points.
Apple has also seen its smartphone market share decline against competition from rivals such as Samsung.
In the third quarter of 2012, Apple held just 14.6% of worldwide smartphone shipments, down from a peak of 23% in the fourth quarter of 2011 and the first quarter of 2012, according to IDC.
By contrast, big rival Samsung's share of smartphone sales has risen strongly over the last two years, from 8.8% from the third quarter of 2010 to 31.3% the third quarter of 2012.
The Korean firm is expected to launch the new flagship Galaxy S4 smartphone in April this year, followed by the Galaxy Note 3 smartphone-tablet hybrid and a series of other phones of various incarnations over the year, according to current speculation.
It operates a more diversified strategy with its mobile devices compared to Apple, which currently releases just one new version of the iPhone every year, with the iPhone 5S or iPhone 6 expected in the autumn.
However, Apple boss Tim Cook has already showed a willingness to break with Apple's previous product strategy, as in October last year he introduced a cheaper and smaller version of the iPad, called the iPad Mini.
The iPhone is Apple's biggest revenue driver, accounting for 48% of its earnings in the quarter than ended September 2012.
According to The Wall Street Journal's sources, Apple developed designs for a cheaper iPhone in 2010, before it launched the iPhone 4.
However, some of its executives were worried about a second iPhone complicating the manufacturing process, and instead opted to sell older iPhone models for cheaper prices after its annual product refresh.
Releasing the iPhone Mini in 2013 or 2014 could help the firm make greater in-roads into the mid-level and entry-level markets that Android devices now dominate.
It could also help Apple build new customer bases in emerging markets such as China and India, where consumers are less able to afford the high upfront cost of a new iPhone.
The history of the iPhone in pictures:
Copyright: PA Images Paul Sakuma/AP