I can't possibly give you an answer to such a vague question, especially when I'm not the only person you were speaking to.
Let me give this a bash.
If the universe is still expanding, then that means that it is finite, yes? If it was infinite, it wouldn't be expanding. It would just be.
The prevailing theory currently is that the universe is constantly expanding and that it will continue to do so. But even if it always, forever, expanded, it would still be finite because, again, if it weren't finite, it wouldn't be expanding.
What I mean by near-infinite is that the universe is constantly striving toward this state, but that it will never attain it.
It is theorised that outside of our bubble of finite-ness there is infinity. Even if one has the outside of our universe in mind, one must consider things with this proviso: the rules, the math and the science, that applies to our universe could well not, outside of it.
So is there such a thing as infinity? Maybe, and maybe not.