According to the guys over at BrokenJoysticks, Splatoon 2 will feature singleplayer campaign. Their source is a Nintendo rep they spoke to at a recent Switch press event.
The original Splatoon had a singleplayer mode, but not an actual singleplayer campaign. The singleplayer mode was mostly to teach players how to play online.
According to the source, Splatoon 2 takes place 2 years after the original game. Singleplayer content was sort of hinted in the Splatoon 2 trailer, but Nintendo never officially confirmed it.
Splatoon 2 will be released this Summer on the Switch.