Los Angeles Times said the demand comes during rising uncertainty about whether Chavez is healthy enough to remain in office.
Opposition leader Ramon Guillermo Aveledo said that if Chavez is too ill to return from Cuba, where he underwent surgery last month, the government should call an election within 30 days.
Vice President Nicolas Maduro told a TV interviewer in Cuba Tuesday that Chavez remained in "delicate" condition and was suffering from a respiratory infection.
Maduro did not say whether Chavez will return to be sworn in for a fourth term, and Chavez has never said what type of cancer he has.
The Los Angeles Times said that Chavez supporters have proposed postponing the swearing-in to give Chavez more time to recover.
If Chavez resigned, Maduro would assume office until Jan. 10, and then the National Assembly president would become the leader until a new election could be held.