Charles Sale over at The Daily Mail claims that the US company will enter the fray when the rights come up for tender before the end of the current season.
Apple - the most valuable technology firm in the world - is said to view Premier League football as the ideal type of premium content to draw UK users to the Apple TV service, utilising the iTunes subscriptions infrastructure already in operation.
Sale also believes that Google will be interested in the rights for its Google TV service, which is due to launch in the UK and Europe this year.
Apple is widely rumoured to be developing new branded internet-connected television sets for launch this year, as part of the firm's "assault on the living room".
The company has so far taken a tentative approach to the TV market, with Apple TV selling only around 2m units since March 2010, compared with the more-than-40m iPads shifted by Apple.
But the TV market is now hotting up, and the likes of Google and Apple see long-term revenue-generating opportunities in connecting consumers with large libraries of pay-TV content.
Sale feels that the involvement of the US giants in the Premier League TV bidding could create a competitive market at a time when other TV sports are in decline.
Sky, which paid £1.6 billion for its current TV rights deal, will definitely be in the running again for the rights, while the Disney-owned ESPN - which picked up packages after the collapse of Setanta UK in 2009 - has already signalled that it will be involved.
Sale also feels that Middle East network Al Jezeera may have the resources and the interest to break Rupert Murdoch's stranglehold over Premier League TV rights.
The Football Association had to accept a 30% drop in the price of its two-year FA Cup and England games deal renewal with ITV last year.
But the Premier League has been a very effective negotiator at getting a good price for its TV rights, and the next auction is expected to be equally lucrative.
With in excess of $70 billion in cash reserves, Apple certainly has the funds to rival Murdoch for the Premier League, but it seems hard to believe that Sky would allow one of its crown jewels to be taken by a new rival.
However, it could be that the League could instead look to create special packages of on-demand highlights for Google and Apple to be made available on their platforms.