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The Pogues are battling for number one along with Wham! and Mariah Carey after the death of frontman Shane MacGowan, the Official Charts Company says.
Their gritty festive track Fairytale of New York has never reached the top spot since its release in 1987.
Last Christmas by Wham! is currently on track to take the top spot next Friday.
Carey's All I Want for Christmas is You has climbed from sixth to second. But The Pogues' rise to third spot puts them in the running for Christmas.
The rise of 15 places in seven days puts them in contention for the coveted festive number one spot to be announced on 22 December.
Fairytale of New York peaked at number two when it was released after being beaten to the Christmas number one slot by the Pet Shop Boys' Always on My Mind.
After MacGowan's death, aged 65, on Thursday, his wife Victoria Mary Clarke told the BBC she would love to see the song at the top of the charts.
"It would be nice, wouldn't it?" she told BBC Radio 4's Today programme. "It should be the Christmas number one, it absolutely should. I'm very much in favour of that."
Fairytale of New York was written by MacGowan with fellow Pogues founder Jem Finer and was later re-recorded to have the late Kirsty MacColl duet with MacGowan, which led to the best-known version of the track.
It has returned to the top 40 every year since 2005.