You made mistake in title. "Are both these two correct?"

The second sentence is the one which is gramatically correct - ie it has the correct tense - but few people know this, or bother to use it! The first sentence is overwhelmingly more common in spoken language.

"were" is correct. Whenever we imagine something we use "were" in this kind of sentences irrespective the subject. examples-- If he were here. If they were here. If Alex were an engineer. If she were a doctor.