Nelson's camp wasn't immediately available for comment, but Carwin's camp informed MMA Fighting that they have yet to be offered a fight against "Big Country."
However, other sources close to the fight, have confirmed with MMA Fighting that the organization is looking to match up the heavyweights at UFC 125 on New Year's Day.
The only potential issue is if Nelson doesn't fully recover in time from knee surgery. The former IFL champion went under the knife immediately following his loss to Junior dos Santos at UFC 117, and it is still unclear whether or not he will be ready to compete again in three months.
If Nelson isn't cleared to fight, there is also a chance the fight could be pushed back a month.
Carwin and Nelson traded shots over Twitter in August, leading to many fans hoping to see them fight sooner than later.
Speaking of Twitter, Carwin tweeted on Tuesday that he expects to be fighting on the Jan. 1 card. He is coming off a title loss to Brock Lesnar in July.
A lightweight title fight between champion Frankie Edgar and Gray Maynard is expected to headline UFC 125 in Las Vegas.