The Wall Street Journal claims that the talks represent Apple's "most ambitious crack at infiltrating the living room after years of trying".
Apple has long hoped to create a more complete television device as a way to create a foothold in the living room, after enjoying huge success with its mobile devices such as the iPad and iPhone.
The firm has offered the Apple TV device for several years, but the box just streams HD video and not live television, meaning it has largely been viewed as just a 'hobby' for the world's biggest technology company.
A major obstacle preventing Apple from launching a broader TV product has historically been the reluctance of broadcasters and operators, particularly in the US, to allow the firm to gain a significant foothold in the market over fears that they will lose control of revenues.
The paper says that Apple could create its own set top box that can receive TV signals from the operators. This would mirror its successful strategy with the mobile phone industry, in which it sells the iPhone to customers but then relies on carriers to provide the phone, text and data signals.
Apple declined to comment on what it deemed rumour and speculation.
But Apple chief executive Tim Cook is understood to have met with Glenn Britt, chief executive of Time Warner Cable, last month during a media conference to discuss the firm's television plans.
It is unclear whether Apple is discussing an iteration of the existing Apple TV, which sold 1.3 million units in the second quarter of this year, or an entirely new device.
Cook recently said that the TV market is of "intense interest" to Apple, and insisted in an earnings call that he believes Apple TV "will lead us somewhere". That somewhere could be to an Apple-branded, web-connected flat panel television set.
Apple looked at making a set top box for cable TV in the US before Apple TV launched, but its then chief executive Steve Jobs dismissed the idea due to the problematic negotiations with the operators and entertainment companies.
TV operators have previously been concerned about Apple muscling in on their market, but they may now be persuaded by its reported focus on hardware, which could bring the same kind of boom as seen in the phone market after the iPhone was launched.
Much will depend, though, on whether Apple can bring the required innovation in its hardware, either via a set top box or integrated TV set, to revolutionise the TV industry in the way it has always hoped.