Last year the Nintendo Switch makers went all out to celebrate Mario's 35th birthday.
In the run up to the anniversary of the original Famicom release of Super Mario Bros, Nintendo held a Super Mario 35th Anniversary Direct.
During that broadcast the recently released Super Mario 3D World + Bowser's Fury was announced along with an AR Mario Kart game, a Mario themed Game & Watch as well as Super Mario 3D All-Stars.
Considering the Mario 35th Anniversary was such a big deal, it seems likely Nintendo could mark Zelda's 35th Anniversary in a similar way.
The Zelda 35th Anniversary falls on a Sunday, and while Nintendo has held Directs before on a weekend they usually stick to weekdays for big announcements.