The universe is infinite by definition. It may be closed, which mean it will repeat itself indefinitely, but that's still infinite.

What isn't infinite is the observable universe. But the observable universe is just the view we have, its boundaries are defined by the observer. In fact my observable universe is different from your observable universe, by an insignificant amount.

When physicists talk about the universe, it usually means the observable universe. Simply because for us, that's all we have.