Jay-Z is keeping fans guessing ahead of his highly anticipated Yankee Stadium shows ... but he couldn't dodge TMZ's questions entirely when we caught up with him in New York City on Monday!

Check out the video ... Hov dropped a couple hints about what's in store for his trio of Yankee Stadium shows coming in July and even weighed in on a question fans might be wondering about -- whether he'll keep the afro, switch to braids or bring back his signature Caesar cut.

But before the conversation could go much further, Jay politely shut things down.

As we've reported, Jay's gearing up for Yankee Stadium concerts celebrating milestone anniversaries for "Reasonable Doubt" and "The Blueprint" -- some of his biggest hometown shows in years.

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The concerts come after his recent buzzworthy Roots Picnic set, where fans believe he took aim at Drake, Kanye West, and Nicki Minaj during a viral freestyle.

For now, Jay's not showing all his cards ... but he let us know the work is already underway!