Aye, they can like.
There is a standard clause in pretty much every manager's contract that stipulates they aren't allowed to bad mouth the club in public - if this leak has come direct from Rafa and the club are able to prove it, they could sack him.
Not that they would like, but it can and does happen. I'd imagine Rafa is clever enough to ensure the link has come from someone that isn't himself like, such as an associate.