The pair could meet in the quarter-finals of the tournament at the York Barbican, which would re-ignite the feud set ablaze at the Australian Goldfields Open earlier this season when Northern Ireland's Allen accused Bingham of having "no bottle, no balls" and the Essex player responded by calling his rival "an idiot."
Bingham won their quarter-final tie Down Under and went on to win the tournament, beating Mark Williams 9-8 in a dramatic final to land his first ranking title.
Anticipating a possible last-eight clash in York, Bingham said: "The rivalry is not going to disappear. I've seen him at tournaments but not spoken to him. Neither of us are going to say hello to each other. Until the next time I play him, I'll keep away from him.
"It's just one of those things that is unlikely to go away. After I lost in the quarter-finals of the PTC event in Killarney, someone on Twitter wrote 'no bottle'. So it looks like people aren't going to forget about it either.
"He did me a favour before our match in Australia because I forgot about the fact that I was playing for my first semi-final, I was just focussed on beating him. I felt good about it after the match, but then after I beat Shaun Murphy to get to the final, I broke down and all the emotion came out."
Bingham is into the top 16 of the world rankings for the first time so earns an automatic place at the UK Championship. He faces Hong Kong's Marco Fu in his opening match on Sunday December 4 at 11am.
"I've been plugging away in the qualifiers for 16 years so it's great to be at the venue automatically now," said the World No 12, who beat Ronnie O'Sullivan in the first round of the UK last year. "I've got a decent record in it and hopefully I can improve on that."
"I can't wait to be in that situation of having the chance to win a tournament again, and I won't be afraid of losing."
The UK Championship runs from December 3 to 11, with the likes of Ronnie O'Sullivan, John Higgins, Judd Trump, Stephen Hendry, Steve Davis and Mark Selby battling for the £100,000 top prize.
From the World Snooker website.
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