The row centres on the price Sky should pay to offer live football action to British Digital Broadcasting.
Sky tied up a long-term programming deal with BDB, owned by Carlton Communications and Granada Group, after it had to drop its equity stake for competition reasons.
Premier League games are a key part of Sky Sports, one of the channels on offer from BDB, but Sky's existing four-year pounds 670m deal with the League does not cover digital terrestrial television.
Sky will have to negotiate an additional contract with the league to enable BDB subscribers to access games shown on cable and satellite television.
City analysts believe Sky is unwilling to pay more than pounds 50m for rights to show Premier League action on digital terrestrial until 2001, when Sky's contract with the league comes up for renewal. However, the league is thought to be pushing for at least pounds 70m.
A spokesman for the Premier League said: "The development of digital terrestrial is clearly over and above the current agreements. Broadcasting the Premiership games cannot occur without the explicit agreement of the Premier League."
He added: "Broadcasters cannot expect to earn vast sums of money from the transmission of our games without football seeing some of the benefits."
According to a report published today by the stockbroking firm Henderson Crosthwaite, Sky will succeed in negotiating the rights, "but at a price".
However, a source close to Sky said it would not be worth paying over the odds for the Premiership as viewing figures for digital terrestrial television would be low at first.
According to estimates from Henderson Crosthwaite, BDB will capture 1.2 million subscribers by the time Sky's contract with Premier League comes up for renewal in 2001.
Although Sky does not have the first option on negotiations with the league for digital terrestrial, the satellite operator does have a "holdback" clause which prevents the league agreeing a deal with another broadcaster.
An auction is therefore virtually out of the question. Even so, the league has approached other broadcasters to sound them out on how much the digital terrestrial rights are worth.
The disagreement is thought to have been triggered in part by the arrival of a new chief executive at the Premier League, Peter Leaver. While Mr Leaver has publicly emphasised that "there is no weakening of the link" between Sky and the league, industry sources say he is keen to secure a fair payment for the digital terrestrial rights.
A period of protracted squabbling over the rights will do nothing to help Sky's share-price, which has been battered in recent weeks by news of the resignations of Sam Chisholm, the company's chief executive, and David Chance, his deputy.
Sky's enforced withdrawal from BDB has also depressed the stock.
The report from Henderson Crosthwaite, entitled Digital TV: the Implications, sees further troubles ahead for Sky: "We continue to believe Sky is overvalued. It will face intense competition in the digital age and further regulatory restraints."Reuse content