U.S. stocks could climb a bit higher, but the dollar will have no such luck, says Peter Schiff, CEO of Euro Pacific Capital.

"Although I don't think there's a lot more upside in the stock market, I'm not looking for a collapse," he tells CNBC.

"But what I am looking for is a dollar collapse, so that even if the market continues to move higher, it's nominal highs only. It's not real highs adjusted for a loss of purchasing power in the dollar."

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The Standard & Poor's 500 Index stood at 1,880.93 Friday morning, after reaching an all-time peak earlier.

Continued easing by the Federal Reserve will push the dollar down, Schiff argues. "As the Fed has to print more and more money to keep these asset bubbles inflated, it will diminish the value of the dollar."

Schiff notes his antipathy for the dollar is keeping him from selling stocks. "Being short the stock market is like being long the dollar. I don't want to borrow dollars to short U.S. stocks, so I don't have short positions."

He recommends gold and other commodities as a hedge against inflation. "I don't think the stock market is going to be a perfect hedge."

Not everyone shares his bearishness on the dollar. "The market perception that the Fed will always be dovish was wrong. We remain bullish on the dollar," Athanasios Vamvakidis, head of Group of 10 currency strategy at Bank of America, tells Bloomberg.

"If we start to get good U.S. data, the market will be much more comfortable [buying the] dollar."

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