Two sources familiar with the matter told the Reuters news agency the wide port - which has been a standard on Apple gadgets for nearly a decade - would be discontinued.
The aim is apparently to make room on the bottom of the device so the earphone jack can be relocated from its current position on the top of the phone.
But it also means the new phone would not connect with standard docking stations without an adapter.
According to the unofficial Apple news site iMore, Apple will be making an adapter available - although it is unclear if this will be bundled with the iPhone 5 or just sold as an accessory.
The Reuters sources said the iPhone 5, Apple's next generation iPhone, which is expected to go on sale around October, would come with a 19-pin connector port at the bottom instead of the usual 30-pin port.
Some analysts queried why Apple had not switched to something like microUSB earlier, but the company has always taken a very individual approach to its technology and operating systems.
And while microUSB would make sense, the new connector is likely to be unique to Apple.
According to sources on another independent Apple news site, iLounge, the new connector is said to be "closer to a pill shape".
"It represents an opportunity for accessory vendors," said Pete Cunningham, a London-based analyst at technology research firm Canalys.
"The iPhone connector has been a standard for a long time now and I would expect the same to be true for a new connector, should Apple change it as expected."
Tech blogs have long speculated on the demise of the 30-pin connector, which at 21mm wide takes up a relatively large amount of space.
The latest technologies, such as microUSB, offer more power in less space.
A smaller connector would give Apple more scope for new product designs or a bigger battery - or just to make ever smaller products.
Logitech, which is one of the biggest makers of Apple speakers, declined to comment on the claims.
But some enterprising vendors in China have already begun offering cases for the new phone, complete with an earphone socket on the bottom and a supposed "guarantee" that the dimensions are correct.
"Apple needs to find a solution not to disappoint their current clients who want to upgrade to the new iPhone but are tied to an expensive accessory they have bought," said Francisco Jeronimo, an analyst at technology research firm IDC.
"I believe Apple will come up with some sort of adapter so the new iPhone can be used with previous connectors."
But some iPhone owners questioned whether even an adapter would help.
"With a smaller connector, what am I going to do with my loudspeaker at home and the fitness pack that I use when I go to the gym? That's the question," said 24-year old Travis Tam, who owns an iPhone 4.
"I feel that the premium gap between the next iPhone 5 and newest Android models is getting much smaller these days.
"That will mean that details such as having a smaller connector will mean more in whether I will continue to use an iPhone and switch to other Android phones."