J-Rod eyeing tallest residential building in Western Hemisphere

Jennifer Lopez and Alex Rodriguez have upped their home-hunting game.

The couple has been circling an apartment at 432 Park Ave., the tallest residential building in the Western Hemisphere.

“They have been at the building four times,” a broker said.

One unit they are looking at is a four-bedroom, half-floor unit on a high floor, another broker told The Post.

The building makes sense for the famous couple: Lopez has moved her 9-year-old twins with ex-husband Marc Anthony to a Catholic school on the Upper East Side.

“Living in Midtown would be much more convenient for them,” a source said. “But it is far from a done deal — there is no contract out on the apartment yet.”

Still, the home hunt is so serious that Lopez has already listed her NoMad penthouse for $27 million.

There would appear to be a number of possibilities at 432 Park: A four-bedroom unit on the 56th floor is on the market as a $69,500-a-month rental.  There’s also an $82 million penthouse on the 95th floor that comes with six bedrooms. If that price is too high, there’s a $40.5 million three-bedroom available on the 87th floor, according to Streeteasy.com.

The 96-story building rises to a height of 1,396 feet. It was designed by architect Rafael Vinoly.