The recent detection of possible neutrino emission from the blazar TXS 0506+056 was the first high-energy neutrino associated with an astrophysical source, making this special type of active galaxies promising neutrino emitters. The fact that two distinct episodes of neutrino emission were detected with a separation of around 3 years suggests that emission could be periodic. Periodic emission is expected from supermassive binary black hole systems due to jet precession close to the binarys merger. Here we show that if TXS 0506+056 is a binary source then the next neutrino flare could occur before the end of 2021. We derive the binary properties that would lead to the detection of gravitational waves from this system by LISA. Our results for the first time quantify the time scale of these correlations for the example of TXS 0506+056, providing clear predictions for both the neutrino and gravitational-wave signatures of such sources.
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