Forward, yes, easily.

Backwards, maybe, but not easily.

Before we can ever find out if we could send information backwards in time, we will need to discover and utilize negative energy, which is a theorized form of energy that has not been proven to exist although mathematical models hint at the possibility of its existence.

At the same time though, those mathematical models are abstractions that attempt to correlate real-world information with theoretical frameworks and because of that there are margins of error that we cannot currently determine in those mathematical models.

Further, new information that comes out as we continue to explore the universe may invalidate those mathematical models and replace them with a more accurate mathematical model.

That information may completely eliminate the possibility of the existence of negative energy.

Finally, even if negative energy is proven to exist or something close enough to it that it fills the Gap in the mathematical models correctly, there is no guarantee that we can harness that energy and use it to send information backwards in time.

However, I am saying that there is a chance, but it is exceedingly doubtful and probably a very very long time away.