"żadny" somehow is not an existing form, although it would follow the usual rules. But the right masculine singular form is "żaden".
"żadnym wywiadem" - well, that is correct on its own, but it's Instrumental, so let's say "Ta rozmowa nie będzie żadnym wywiadem" = "This conversation will be no interview! Just two people talking, completely off the record!".
"Nie będzie mieć żadnego wywiadu" - also 'somewhat possible', but that just literally means "He/She won't have any interview".
So "nie będzie" is simply the Future Tense of "nie ma", even if the verb happened to change.