Facebook’s Mark Zuckerberg is eyeing a 107-year-old post office on Manhattan’s West Side to help him grow the social networking giant’s Big Apple presence, The Post has learned.

The Menlo Park, California, tech giant is in talks to lease all 740,000 square feet of office space being built in the former James A. Farley Post Office — located across from Madison Square Garden, sources said.

The landmark building, which has been renamed the Farley Building by its redeveloper, Vornado Realty Trust, is slated to open next year following a gut renovation.

No deal has been signed, but talks are advanced enough that the US arm of Japanese advertising firm Dentsu has been derailed from its play to take over the fourth floor, sources with knowledge of the talks told The Post.

The grandiose post office building, which occupies an entire city block, was built in 1912 along with the original Pennsylvania Station — and is widely recognizable thanks to its all-white facade and Corinthian colonnade.

The building, which was designated a New York City landmark in 1966, was reported to be the largest post office in the country when it was built on the block bounded by West 33rd and West 34th streets between Eighth and Ninth avenues.

The stunning exterior will remain largely the same post-renovation. Inside, high-tech office space will take over floors 2, 3 and 4. A smaller fifth floor, which Facebook will also lease, will be added atop the building surrounded by 70,000 square feet of outdoor landscaped park areas.

Tenants will have direct access to LIRR and Amtrak trains through a newly built train hall under the building, along with restaurants and shops on the ground floor.

Crain’s previously reported that Facebook is looking to lease office space at the nearby Hudson Yards buildings, including Related’s and Oxford Properties’ 50 Hudson Yards, which won’t be finished until 2022, and the already-opened 35 and 55 Hudson Yards.

Sources tell The Post that Facebook isn’t giving up Hudson Yards for the Farley Building. Rather, it is looking to lease both spaces, which are roughly two blocks apart on Manhattan’s West Side.

It’s unclear what will happen to Facebook’s current NYC offices, including 758,000 square feet at 770 Broadway and 266,000 square feet at 225 Park Avenue. So.

Both Farley and 770 Broadway are owned by Vornado and its chairman Steve Roth, who has been wining and dining tech companies for years in an effort to lease them the top floors of the post office.

Roth, whose reps didn’t immediately return a request for comment, could cut Facebook a deal for Farley that also lets it off the hook for its current East Village lease, which expires in 2025.

Neither Facebook nor Dentsu respond to requests for comment.

If Facebook takes over the Farley Building, the Far West Side of Manhattan will cement its position as the new Silicon Alley. Google is spending $1 billion for a new campus just south of the West Village, while Amazon has offices along West 34th Street.