They don’t get much more anti-American than Venezuela’s Hugo Chavez.

For many Americans, the Latin American president is embodied by his 2006 lashing out at then-U.S. President George W. Bush.

“Yesterday the devil came here and it still smells of sulfur today.”

For the United States, the socialist Chavez has been a diplomatic troublemaker ever since he took office for the first time in 1999.

But that doesn’t mean the United States has given up on Venezuela. Especially with Chavez — who is undergoing cancer treatment in a Cuban hospital and battling complications — being too sick to attend his own inauguration for a new six-year term.

Asked Thursday to comment about Chavez, State Department spokeswoman Victoria Nuland told reporters that the United States has “put forward some ideas about how this relationship could be improved on a step-by-step basis.”

“Our sense is that at the moment they are very much preoccupied with internal affairs,” she said. “So we are standing by and when they are ready to talk to us about improving things, we’re ready for those conversations.”

For 14 years, Chavez made it his mission to lambaste the United States for meddling in his country and the region. But Washington does want a better relationship with Venezuela, the fourth biggest supplier of oil to the U.S., providing 10% of oil imports into the U.S.

There are several things, Security Clearance has learned, that the Obama administration wants to work with Venezuela on, including counter-narcotics efforts, fighting terrorism, energy and the rule of law.

But Washington is taking a go-slow approach. After all, even when Chavez is gone, his left-wing ideology, “Chavismo,” will live on at least for a while. And his supporters, the “Chavistas,” hold all the major levers of power in the country.

“He controls the courts and the media and other institutions,” said Michael Shifter, president of the Inter-American Dialogue and adjunct professor at Georgetown University’s School of Foreign Service. “There are a lot of Venezuelans who view him very sympathetically, see him as the savior of the country even though the conditions are very, very bad in the country.”

The U.S. has been talking with Venezuelan officials as well as officials from other Latin American countries during the past few weeks and that has fueled speculation that Washington is trying to engineer a transition to a leader more friendly to the United States. Memories run deep of a coup in 2002 that removed Chavez from office for 48 hours. He blamed the U.S. for trying to overthrow him but Washington has always denied any involvement.

The State Department insists it’s strictly hands-off.

Washington wants a “democratic … transparent” transition, Nuland said, adding that “it’s going to be for Venezuelans to decide how that happens.”

Shifter said the U.S. is watching from afar.

“I don’t think there is any evidence the United States is up to anything,” he said. “I think it would be counter-productive. The Obama administration has been very restrained in its position toward Venezuela and has been very careful, I think, to just let the situation play out.”

Chavez is friendly with Iran, North Korea, Belarus and Syria but, in spite of that, commercial ties between the U.S. and Venezuela are strong.

“The U.S. is Venezuela’s most important trading partner, with U.S. goods accounting for about 24% of imports and approximately 42% of Venezuelan exports going to the United States,” according to the State Department.

Venezuela has played a game of musical chairs with ambassadors.

More than four years ago, Chavez ordered the expulsion of the U.S. ambassador. In return, the U.S. kicked out the Venezuelan ambassador.

A year later, both ambassadors returned to their posts, but in 2010, the Venezuelan government refused to accept the credentials of the new U.S. ambassador. Washington took the same action against the Venezuelan ambassador.

Even if relations improve, don’t look for the U.S. to send its ambassador back anytime soon. Chavez, by some reports, is nearing death, but “Chavismo” is still alive and well in his Venezuela.