Hauer and Westlife's Nicky Byrne were eliminated from the BBC One ballroom reality show, losing out in a dance-off to Van Outen and Jordan.
According to the Daily Star, Hauer had a dig at the rival duo when the show ended, describing Van Outen as "all jazz hands, teeth and no substance".
James Jordan apparently responded angrily, telling Hauer: "Keep your comments to yourself."
Speaking after his elimination last night, pop singer Byrne said: "It has been just so much fun. It is the biggest and best show in the world. To come out every Saturday night is hard, but it's playing a different character, doing a different dance - it's just been amazing.
"Karen, every week, every day has been incredible. We had a bit of a shaky start in terms of judges and stuff, but we just seemed to improve. I have to say thank you to the judges - you have been absolutely amazing with all your advice, all the people backstage - even the people that get you your coffee - I am going to miss the whole thing, it's been an amazing experience."
Strictly Come Dancing's semi-final airs next weekend on BBC One.
Strictly Come Dancing Show 11: