Talking to Newsarama, Marvel SVP Publishing Tom Brevoort told them,

Nrama: So there won't be a new Avengers or New Avengers series on comic shelves in May? Or during Secret Wars' run? Brevoort: Correct. That'll continue as far as we know it. There won't be anything in June either. Beyond that, who knows.

Well, the usual event would be a new Avengers #1 in July. But as Tom says, who knows? Newsarama also had some rumour questions.

Nrama: And seeing Reed and Sue in such prominent roles in Marvel's biggest storyline currently – what would you say to the rumors that Marvel is phasing out the Fantastic Four? Brevoort: It really doesn't matter what I say. People are going to believe what they choose to believe, and people are going to make hay out of stirring the pot and fanning the flames – planting and harvesting that click bait. What we do is tell stories with all the Marvel Universe characters, as we have all along. Certain people have gotten nervous to the point of craziness, but the proof is in the books we're putting out. I could literally say anything, but it won't make any difference. People are just afraid, and let fear overwhelm them.

Just so people know, Bleeding Cool didn't run rumours that Marvel are phasing out the Fantastic Four, Just that they would appear in other titles rather than their own Fantastic Four book.