The BBC says it is yet to decide whether to play Ding Dong The Witch Is Dead which mocks the death of Margaret Thatcher during the Radio 1 top 40 countdown.
The song from the Wizard Of Oz has been climbing the music download charts after anti-Thatcher campaigners encouraged people to buy it in the wake of the former prime minister's death.
The tune is already in the top five ahead of the weekend's Official Chart Show results.
Some reports say Radio 1, which has a target audience of 15 to 29-year-olds, is planning to play the track on the countdown and could have a reporter explain to listeners why the 1939 song is in the charts.
In a statement, the BBC said: "The Official Chart Show on Sunday is a historical and factual account of what the British public has been buying and we will make a decision about playing it when the final chart positions are clear."
Speaking to Sky News, the Sun's political editor, Tom Newton Dunn, said the BBC was "in a very difficult position".
He said: "It's an incredibly hard decision to make. They have to balance freedom of expression, the right to protest - albeit it very rudely - on one side, and also people's right not to be offended when listening to a simple chart show.
"It's a hugely offensive song and it's offensive that people are buying it - it's childish, but they also have a right to do that and say that.
"There are a lot worse things that you can do and if people want to be rude to a certain level then that is their right."
If the BBC decides to ban the song, it will not be the first time that the corporation has censored the airwaves.
Both the BBC and the Independent Broadcasting Authority, which was responsible for regulating commercial broadcasting, refused to play the Sex Pistols' God Save The Queen when it was released during the Silver Jubilee in 1977. The song reached number two in the charts.
The BBC also banned Frankie Goes To Hollywood's 1983 single Relax from both radio and television after deciding it was too obscene, but it went on to reach number one in January 1984.
In 2007, Radio 1 bleeped out some of the words on the Pogues' Fairytale Of New York to avoid offence, but it later reversed its decision after listeners complained.