There are interpretations of quantum mechanics that make related claims. There's the transactional interpretation, proposed by John Cramer and developed more recently by Ruth Kastner. It holds that quantum events such as measurement results occur when there is a "handshake" between an advanced wave, traveling from future to past, and a retarded wave, traveling from past to future. The so-called two-state vector formalism, pursued in recent years by Yakir Aharanov and Lev Vaidman, is in some ways similar. Huw Price has long argued that if we allow for backward causation, we can avoid having to posit faster-than-light action at a distance. Some people have argued that in certain cases, quantum teleportation involves information moving from future to past.
But all of this is controversial and it would be hard to argue that a consistent understanding of quantum mechanics requires backward causation. To which we should add: these interpretations do not claim that quantum mechanics can exploit any such backward causation to allow someone in the future to send messages to us in the present. In other words, if there's information from the future that impinges on quantum events in the present, it's not "available" in the sense of being something we can extract and make use of.