Mr Skinner's management company, Avalon, was asking for nearly pounds 20m for the comedian to sign up exclusively to the BBC for five years, BBC sources said.
Meanwhile, Sky added Mr Skinner's comedy partner, David Baddiel, to its collection of BBC deserters, paying pounds 5.5m for a new sitcom written by, and starring, the comedian.
Sky recently spent pounds 1m to lure Harry Enfield from the corporation and has now committed itself to 22 episodes of Mr Baddiel's show, provisionally entitled Baddiel's Syndrome.
Alan Yentob, the BBC's director of television, said that the comedy situation was getting out of hand: "The BBC offered what we think is a generous price for a new and wide ranging deal with Frank. But we were not prepared to agree to Avalon's unreasonable tactics and financial terms. Even in the most competitive market place there come demands which are so ridiculous that you have to walk away."
Sky said it aims to make a comedy on the American model, with a view to selling it in overseas markets. "For a long time, British broadcasters have been told by Americans that they don't commission the right amount of episodes for US television," said a spokesman.
"Friends, Seinfeld and Frasier all began with a minimum of 22 programmes - while the British comedy yardstick has been six half-hours."
British runs are shorter because comics here tend to write alone, while Americans write in teams. Mr Baddiel is known to have been keen on the longer commitment in order to ensure greater character development, and to allow the show to find its audience. If he completes 22 episodes alone, it will be something of a record.
"The central character is in therapy," Mr Baddiel said. "Each week he starts to tell his therapist, who's fairly disturbed himself, how things have panned out this week. Then we cut to the action. At the end of the show, we come back to the the rapist."
The programme will also feature an American comedian who "is a household name on both sides of the Atlantic," said a spokesman for Avalon, which will produce the show. However, a contract is still three to four weeks' away.