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Roger Federer Says Zverev Is Next Big Thing, 'Gonna Make Life Difficult!'

Roger Federer knows he ain't gonna be the best forever ... and he's revealing to TMZ Sports his biggest threats to the throne -- and one of the guys just helped Fed break a huge record!!

We spoke with the 38-year-old superstar out in NYC and asked straight-up which young guns are giving him the biggest headaches ... and Federer name-drops 2 dudes he's got in the rearview -- 22-year-old German Alexander Zverev and 21-year-old Stefanos Tsitsipas from Greece!!

Of course, Federer and #7 Zverev just broke a major attendance record when more than 42,000 people showed up to watch their exhibition in Mexico City over the weekend.