New York (CNN Business) It's no secret that President Donald Trump wants to weaken the US dollar to juice the American economy.

Trump has repeatedly suggested the greenback is too strong against rival currencies -- and some analysts say he's probably right. The US dollar may in fact be overvalued, depressing overseas trade and manufacturing activity in the Rust Belt important to Trump's re-election chances.

There's growing speculation that Trump officials will take concrete steps aimed at knocking down the dollar, making a sharp and potentially-dangerous break from recent US policy. However, it's not clear how effective such a strategy would be -- and there's a risk it could badly backfire by sparking retaliation from other countries, driving up import prices and weakening the purchasing power of American households.

"It could trigger a currency war," Bank of America warned in a recent note to clients.

The administration has several ways it could weaken the dollar. One would be to explicitly abandon the strong-dollar policy that has been in place for more than two decades. Or Trump could order the Treasury Department to sell dollars in a bid to lower their value. That type of intervention hasn't happened since 1995.

"We think direct FX intervention by the US is a low but rising risk," Goldman Sachs strategist Michael Cahill wrote in a note to clients.

Trump's sudden trade moves have "created a perception that 'anything is possible,'" Cahill said.

The president has already hinted at a bold step on currencies.

On July 3, Trump complained in a tweet that China and Europe are playing a "big currency manipulation game."

"We should MATCH, or continue being the dummies who sit back and politely watch," Trump tweeted.

Any attempt by the Treasury to intervene unilaterally would be bound to fail, unless it could rely on the Fed's support." Paul Ashworth, chief US economist at Capital Economics

Last month, Trump complained that the European Central Bank's easy money policies caused the euro to tumble, "making it unfairly easier for them to compete against the USA."

Of course, the Federal Reserve's own head-spinning shift from hawkish to dovish has cooled off the US dollar. The greenback is up less than 1% this year against a basket of currencies.

The king of the currencies

There is evidence that Trump is right about the dollar. The Economist's Big Mac Index , released last week, showed that nearly all currencies are undervalued against the dollar.

"Trump probably does have a little bit of a point," said Stephen Gallo, European head of FX strategy at BMO Capital Markets.

The US dollar, as measured against a basket of currencies, took off in mid-2016 and has remained relatively high. Those gains reflect economic weakness elsewhere around the world. The dollar has also been boosted by Trump's own policies, including stimulating the US economy with tax cuts and deregulation and efforts to cut the US trade deficit.

"The America First narrative that Trump is pushing is ultimately dollar positive," Gallo said.

The other factor is that the US dollar is the world's reserve currency. That status creates persistent demand for the greenback, making it difficult to properly value the currency.

"The dollar is at the top of the food chain," said Gallo.

Trump himself has acknowledged this, tweeting on Thursday that the dollar is "by far the most dominant currency anywhere in the World, and it will always stay that way."

Is America's strong dollar policy at risk?

Still, Trump officials have tried talking down the dollar in the past -- moves that Goldman Sachs says have had a "decent amount of success."

The easiest way to weaken the dollar, according to Bank of America, is for the Trump administration to announce it is abandoning the strong dollar policy introduced in 1995 under President Bill Clinton.

Such a move "could be very effective," causing the "overvalued" greenback to tumble by 5% to 10% and bringing it back into equilibrium, Bank of America strategists wrote.

Treasury Secretary Steven Mnuchin would not have to declare that the US wants a weak dollar. He could merely say the US wants a fair value for the dollar. Bank of America notes that no other major economy has a strong dollar policy and the US Treasury Department has done "nothing in practice to implement it."

Still, other nations could seek to retaliate against the shift in US dollar policy by weakening their own currencies.

The Fed must go along

A more aggressive option would be an outright intervention in the foreign-exchange market, something that analysts say would break modern norms.

Goldman Sachs said that direct intervention would cause a "sizable market reaction," including a weaker dollar, stronger yen and falling foreign stock markets.

However, the firm warned that there are several complications to such a strategy.

One problem is that Trump would need the Federal Reserve to go along with his plan to weaken the dollar.

Although the Treasury Department has authority over US currency policy, it only has control over a relatively small amount of assets that it could sell in a bid to drive down the dollar. The department's Exchange Stabilization Fund is only sitting on about $22 billion in US dollars, according to Goldman Sachs.

"After accounting for leverage, there are plenty of hedge funds that have more clout than that," Paul Ashworth, chief US economist at Capital Economics, wrote in a note to clients. "Any attempt by the Treasury to intervene unilaterally would be bound to fail, unless it could rely on the Fed's support."

Race to the bottom

Even if the Fed did agree to intervene in the currency market, such a move could take considerable firepower.

Nearly $5 trillion is traded each day in the foreign exchange market, roughly five times the level in 1995 when the US last launched an intervention, according to Ashworth.

"The gorilla keeps getting heavier and heavier," he wrote.

There may be unintended consequences as well. Ashworth said that while depressing the dollar could boost the competitiveness of US exporters in the medium-term, it would also lift import prices and an "almost immediate loss of purchasing power" for American households and businesses.

"We would view any action to deliberately weaken the dollar as negative for near-term GDP growth," he wrote.

Goldman Sachs warned that outright currency intervention could be "counterproductive" if other countries follow suit.

It's easy to see how this could spark a race to the bottom. A currency war, on top of a trade war, is a scary thought. But anything's possible.