The sum is twice the amount of the $30m (£21.2m) fee paid for the TV rights to the blockbuster Titanic, which starred Kate Winslet and Leonardo DiCaprio. TV companies at least got to see the film before they were asked to bid for the rights.
Warner Bros is understood to have approached some of the major US TV networks asking them to bid now. One executive from a major network called the process "obscene", according to a report in Time magazine, which is owned by Warner Bros' parent AOL Time Warner.
TV executives are said to be angry that they are being asked to bid without having seen the whole film.
Warner Bros is said to be showing TV companies just a 15-minute screening of scenes from the film and executives say they have no way of knowing whether the film is going to be successful.
Although fans of the Harry Potter books will undoubtedly watch the film once at the cinema, it is not known whether they will want to watch it a second time on TV.