The Celebrity Big Brother twins, who rose to fame on The X Factor, finished eighth in this year's Eurovision Song Contest with their track 'Lipstick' - beating UK entry Blue.
They dominated European music charts following their appearance, selling 120,000 copies of 'Lipstick' in Sweden alone.
Their popularity has resulted in Irish broadcaster RTÉ asking the twins to perform for a second year in a row at the 2012 contest in Azerbaijan.
"Jedward proved to be one of the most talked-about and popular acts," an RTÉ source told the Daily Star Sunday.
"They were such a massive hit with the media and fans that even the Eurovision organisers requested them back. Provided the song is right, then yes, Jedward will accept the offer."
Jedward, who release new single 'WoW Oh WoW' on November 18, finished third in this year's Celebrity Big Brother.
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Watch Jedward performing 'Lipstick' at the 2011 Eurovision Song Contest below: