The row, which follows similar disputes in recent years in other sports, is centred around how quickly photographers can publish photos when at a game and how live online commentary can be handled.
The media groups believe the rules are out of date at a time when members of the public can access sites such as Twitter and the photo site Flickr during games.
News agencies, such as Reuters, also object to the obligation that media clients who use their pictures from a match have to pay the football authorities for a licence to do so.
The two sides have failed to agree terms despite holding talks for several months, with the news organisations charging that the Premier League wants to place highly restrictive limits on the use of news and pictures produced at matches.
The media groups protesting against the rules include the majority of the national newspapers and news agencies including Reuters and Associated Press.
The Football League, which includes the lower professional leagues, starts a new season this weekend and the Premier League begins on August 13.
"We are unable to guarantee our coverage as the proposed terms and conditions compromise our ability to properly cover and to serve the interests of our clients," Reuters said in a statement.
The Reuters news agency is owned by Thomson Reuters.
The Premier League and The Football League said they had entered the talks in good faith but said the media groups had rejected an interim extension of the existing agreement which was offered to cover the period until a permanent deal was found.
"[They] have not taken up that offer which creates the possibility of disrupted match-coverage in newspapers," they said in a statement. "This serves nobody's interests, particularly not football fans looking forward to the start of the season.
"We remain open to further negotiations and are hopeful of reaching a satisfactory conclusion as soon as possible."
