Sources at the hospital in Cuba where Chavez is being treated told a Spanish newspaper that the president was showing "very weak" vital signs, and that doctors could decide to switch off the machines "at any moment", the Daily Mail reported.
Vice President Nicolas Maduro said the ailing president's condition remains "delicate" three weeks after his cancer surgery.
He did not provide details and told Venezuelans to ignore speculation about Chavez's health.
"He's totally conscious of the complexity of his post-operative state and he expressly asked us... to keep the nation informed always, always with the truth, as hard as it may be in certain circumstances," Maduro was quoted as saying.
Chavez has not been seen or heard from since the December 11 operation, and officials have reported a series of ups and downs in his recovery.
Maduro did not refer to any rumours in particular, though one of them has described Chavez as being in a coma.
He said Chavez faces "a complex and delicate situation". But also said that when he talked with the president and looked at his face, Chavez seemed to have "the same strength as always".
Chavez has been fighting an undisclosed type of pelvic cancer since June 2011. He has declined to reveal the precise location of the tumours that have been surgically removed. The president announced Dec 8, two months after winning the re-election, that his cancer had come back despite previous surgeries, chemotherapy and radiation treatment.
Chavez is scheduled to be sworn in Jan 10 for his new term. If he dies or is unable to continue in office, the Venezuelan Constitution says a new election should be held within 30 days.
Before his operation, Chavez designated Maduro as his successor, telling supporters they should vote for the vice president if a new presidential election was necessary.