New highs for the S&P 500 and Dow Jones Industrial Average are coming into view, but it could take some time before the indices actually get there, analyst Laszlo Birinyi told CNBC on Monday.
"When you have market that started the way this did, consolidated very nicely, and now all of a sudden you're at the exuberant phase, I'm very confident saying that at some point this year 1,600 (on the S&P) is at least a 50 percent probability," Birinyi told "Squawk on the Street."
But first, the S&P 500 may consolidate around the 1,500 level, he said.
In a note to investors, his firm Birinyi Associates wrote, "We would not be too cavalier or comfortable with 1,500 and 14,000," the recent levels for the S&P 500 and the Dow. "While we have a five year high, we are not yet ready to uncork the champagne, although we have put some on ice."
Birinyi Associates disclosed a small long position in SPDR December 160 calls, which is a bet that the S&P 500 will reach 1,600 by December.
(Read More: S&P 500 to Hit 1,600 by Year's End: Analyst)
Birinyi said history is what makes him confident that stocks will push to new highs this year. He said in past bull markets, there is usually one year in the last phase where the market does extremely well, delivering a 20 percent plus return.
This performance happens because investors realize interest rates are not going through the roof, earnings aren't falling to zero and "maybe there won't be another train to catch," he said.