"This will help ensure a smoother leadership transition in Caracas," the officials added.
Venezuela held its last presidential election in October, 2012 which was won by Hugo Chavez.
The call for fresk election by Brazil is a major intervention by Latin America's regional powerhouse that could ensure smooth transition in the country.
Brazilian officials have expressed their wishes directly to Venezuelan Vice President Nicolas Maduro, the officials said on condition of anonymity.
Chavez has designated Maduro as his preferred successor if he loses his battle with cancer.
"We are explicitly saying that if Chavez dies, we would like to see elections as soon as possible," one official said."We think that's the best way to ensure a peaceful democratic transition, which is Brazil's main desire."
Chavez is in Cuba receiving cancer treatment and he has not been seen in public for a month, prompting speculation that he is near death.
Venezuela's constitution says a new election must be held within 30 days if the president dies.
Before leaving for Cuba, Chavez urged Venezuelans to back Maduro should the cancer leave him incapacitated, and Chavez's backers and the opposition appear to be preparing behind the scenes for a possible new vote.
Yet some foreign officials in the region, and some activists in more radical Venezuelan opposition circles, have privately expressed fears that the government could bend the rules if it wants, especially if polls show Maduro might lose.
The Supreme Court's controversial decision to postpone Chavez's inauguration last week reinforced concerns that loopholes could be used to keep the current government in power.
Venezuela's government said on Sunday that Chavez's health had improved somewhat, though his lung infection still requires special care.
Brazil's stance on Venezuela is critical because it is by far Latin America's biggest country and it enjoys growing economic and diplomatic clout in the region.
Its president, Dilma Rousseff, is a moderate leftist whose party has strongly supported Chavez over the past decade.
Yet she is also perceived as neutral and democratic enough to be a credible broker in helping Venezuela chart a path forward if a political crisis erupts.
By clearly supporting a democratic solution now, they hope to dissuade Capriles and others from inciting civil unrest in the event Chavez dies, the officials said.
"We're working very hard to ensure there's peace," the first official said.
Capriles, whom most assume would run against Maduro in an election, has so far taken a relatively subdued tone in spite of the political uncertainty.
He said last week that Chavez's supporters would "win" politically if there was a violent confrontation.
On Monday, the opposition coalition urged the Organization of American States (OAS) to convene a session and give it the chance to address Chavez's absence and recent events it said had "gravely affected the democratic order".
"There is no legal interpretation that justifies the official line about 'continuity'," it said in a letter.OAS Secretary-General Jose Miguel Insulza said last week that the Washington-based organization "fully respected" the decision by Venezuela's top court that backed the postponement of the president's inauguration.
Brazil is keeping the U.S. apprised of its efforts, and is hoping to convince Washington to allow it to take the lead in managing a potential leadership transition in Venezuela.
Chavez is one of the world's most vocal anti-U.S. leaders, and the Brazilian officials said they fear that any direct U.S. intervention in Venezuelan affairs could backfire.
Venezuela's opposition is demanding that Chavez step aside and name a caretaker president while he recovers - but those complaints have so far been ignored by governments around the region, including the Rousseff administration.