The boyband - who finished runners up to Alexandra Burke on the show in 2008 - have been nominated for their song 'She Makes Me Wanna' but if they fail to pick up the prize, they hope someone from the "'X Factor' family" wins.
Singer Marvin Humes said: "If we don't win we'd love to keep it in the 'X Factor' family. Olly Murs is a very good friend of ours, he deserves it, One Direction have had a great year so we'd love someone like that to win it.
"But obviously everyone who's in the category deserves to win, Adele's had a phenomenal year and really showcased British music but we think she's going to sweep the boards at the BRITs anyway so maybe she could leave this one for us or someone from 'X Factor'."
JLS aren't giving up on winning the award and have appointed member Jonathan 'J.B' Gill as their "campaign manager".
Marvin said: "Best British Single is voted for by the public and we've got some tough competition in the category so we've appointed J.B campaign manager to make sure we get the votes to win.
J.B added: "I've said I'm going to wear my Union Jack jumper every day until the day of the BRITs in a bid to win. We're trying to get as many people as we can to vote for us, we're filming voting spots, putting the information up on our twitter and hoping that it works. It's like being in the 'X Factor' all over again, we've campaigned once before, we can do it again."
JLS have teamed up with Mastercard for its exclusive Priceless Duets competition, which supports its 14th year of partnership with The Brit Awards and has seen them perform with one lucky fan.
While JLS's competition is now closed, there is still the opportunity for a Priceless Duet with BRIT award winner Jessie J.
She said: "In the same way my fans have all helped to make my dreams come true, this is my opportunity to do something for them - and make one of their dreams come true too."
For your chance to win a Priceless Duet go to www.somethingforthefans.co.uk