There are no reasons to expect one way or the other. As far as we can measure, spacetime is discrete. However we can't probe very far in the grand scheme of things. Without experimental evidence, and without a particularly strong argument one way or the other, it's useless to be speculating.
Did you mean to say "continuous"?
Quoting Wikipedia , "physical spacetime is expected to be quantum because physical coordinates are already slightly noncommutative."