In March 2015, a judge initially ordered the pair to pay the Marvin Gaye's family more than $7m (£5.3m) in damages for copyright infringement.
The family was also awarded a 50% interest in royalties from Blurred Lines, the biggest single of 2013.
The pair's lawyers are now seeking to appeal against the ruling.
They say the case should never have gone to trial and that the verdict should be overturned, or a new trial ordered.
