Hopefully this is just some fake news from the NY Daily News. That senate seat wouldn't be up that year, so it doesn't even make sense. New York would only have a Senate election in 2020 if someone left office before the election.
Depending on when and if Gillibrand were to resign her Senate seat, there could be a special election that year to fill the seat.
Why would she leave her seat before the election? Bob Dole did in '96, but he was already retirement age. Kerry, McCain, Obama (or VP nominees Lieberman, Edwards, Biden, Kaine...)....none of them resigned before the general election. They all stayed in office until election day, to see if they would actually be elected president. In Obama's case he was elected, and then resigned and had his seat filled by appointment. Presumably, Gillibrand would do the same. She'd only leave her Senate seat if she's elected president or vice president (or picked for the Cabinet), at which time Cuomo (or whoever is governor at that point) would appoint her replacement, right?
