Amazon toured five potential Chicago sites as part of the company’s search for a second North American headquarters and “really liked” two of them, Mayor Rahm Emanuel disclosed Monday.

The mayor did not name the two sites for fear of alienating Amazon, which is evaluating 20 finalists for the 50,000-job mother lode of an economic development prize known as HQ2, for which the city and state have offered a $2.25 billion incentive package.

But other sources said the two finalists are likely to come from the following three: a Chicago River district where Tribune Media wants to build 15 office and residential towers; “The 78,” a 62-acre site at Roosevelt and Clark once owned by convicted felon Tony Rezko, where Rauner dreams of building an innovation center led by the University of Illinois; and the Lincoln Yards site, which includes the old Finkl Steel plant among 100 acres along the River.

The other two sites toured by the Amazon site selection team in March under cloak-and-dagger secrecy were Fulton Market and the Burnham Lakefront, an area that includes the old Michael Reese Hospital site.

The mayor made his comments as he welcomed Walgreens to the old main Post Office. That was one of the 10 sites offered to Amazon that did not warrant a site selection cut.

Emanuel was asked whether Walgreens’ decision to relocate 1,800 employees to the renovated Post Office building, 1,300 of them now working in Deerfield, meant that the Post Office was out of the running for Amazon.

“I don’t want to violate anything with Amazon. … I want to be careful. In our original proposal to Amazon, we had 10 sites. When they came, they saw five sites. It’s our understanding they like — really like — two sites,” the mayor said.

What’s surprising about the mayor’s comment was that Chicago doesn’t even know yet whether it has made what’s expected to be a second cut likely to narrow the Amazon sweepstakes from 20 cities to 10 or even five.

Chicago is almost certain to make that next cut, particularly after former White House Press Secretary Jay Carney, now senior vice-president of corporate affairs for Amazon, emailed the mayor on the January day that Chicago made the cut of 20 cities still in the running for Amazon’s second North American headquarters.

“We look forward to diving deeper on Chicago’s proposal….Everyone here was impressed with the proposal your team put together,” Carney wrote.

Two years ago, Emanuel’s bold threat to seize control of the 2.5 million-square foot behemoth that straddles the Eisenhower Expressway culminated in a court-approved agreement with 601W Companies LLC, to begin a five-year, $500 million renovation and restoration.

Last fall, Emanuel toured the renovated lobby and dusty guts of the Post Office and touted the building as a potential home for Amazon’s second North American headquarters.

Five months later, the City Council signed off on a Class L tax property tax break that’s expected to save building owner 601 W LLC $100 million over the life of the project.

The Class L property tax break allows designated landmarks to be taxed at a rate of 10 percent of assessed valuation for the first 10 years, at 15 percent for the 11th year and at 20 percent for the 12th.

But it’s only available to building owners who agree to invest at least half of the value of the landmark building on an approved rehabilitation project. Eligible expenses include the “core shell and systems” of the landmark building, including mechanical, electrical, plumbing, elevators, exterior walls, structural and masonry work.

The other portion of the assessment — the land portion — is also eligible for the incentive, provided the building has been vacant or unused continuously for the prior two years.

The post office qualified on both counts. It’s been “vacant and deteriorating for more than 20 years” and it’s currently undergoing a gut rehabilitation with a $292 million price tag, Dijana Cuvalo, a preservation architect for the city’s Department of Planning and Development, has said.

The Class L break is expected to save the building owner $100 million over the life of the abatement or $53.2 million in “net present value,” Cuvalo has said.

Even with the tax break, a building that has been vacant since 1996 and paid only $317,000 in property taxes just three years ago is expected to pay roughly $1.3 million in property taxes this year and nearly $20 million just a few years from now, according to City Hall.

“This building is viable and is now gonna come to life after being empty for two decades not only [because] you have the most talented workforce, but the investment in modernizing Union Station makes this a viable option,” Emanuel said Monday.

“I’ve been working on this idea for four years. Once they heard the Union Station piece, that made a concept come to reality.”

Ticking of a list of corporate relocations, including McDonald’s and Peapod, the mayor added, “All of that is because we’re modernizing our transportation system….If it runs on rails, runways or roads, Chicago is leading the country in modernization and it’s leading the country in corporate relocations.”