Legendary investor Bill Miller bullish on Amazon, but sees a struggle for Twitter

Miller: Soft spot in my heart for Netflix

Amazon may be up more than 40 percent over the past year, but legendary investor Bill Miller is still bullish on the stock and the company's prospects.

While Amazon has a market cap of about than $383 billion, the retail in the United States is $5 trillion, the chairman and chief investment officer at LMM told CNBC's "Closing Bell" on Wednesday.

In fact, he foresees a time when Amazon will have a $1 trillion market cap.

"The addressable market for what they're doing is just gigantic," Miller said, noting that Amazon founder and CEO Jeff Bezos told him the addressable market for its Amazon Web Services segment alone is in the "trillions."

Miller believes one of the most misunderstood things about Amazon is when it hits investment cycles. The company does a lot of experimenting, and once it finds something it is convinced can dominate the market, spending goes up, he said.

"That's actually a bullish sign because it indicates they now believe they can actually address another market very successfully."

Miller has long been bullish on the stock, which is one of his company's holdings.

Miller: Twitter needs full-time CEO

He also has a small position in Twitter, which he said is beginning to address its cost issues and is experimenting with different ways to monetize the platform. However, Twitter is losing share relatively speaking on the ad-dollar side, he noted.

"It's a bit of a struggle in here. I think it's a hugely valuable platform but there's very little in the near term that you can see that would be a catalyst to it."

Miller reiterated his belief that CEO Jack Dorsey, who is also CEO of Square, should step down.

He called him a "great entrepreneur, great visionary" who should still be on the board. However, "they need a full-time CEO."