A few reasons to think why:

Dr. Steiner, although "dead", should be a prime suspect for Red John. Sure you'd have to get around the fact that Patrick witnessed him dying, and yes there are a lot of theories about his death being faked, so moving forward with these thoughts we will have to at least assume  that is a possibility. 

Dr. Steiner fits the profile of what Red John is Like physically, as well as his proven mental capacity. Of course if he really was he may not show just how smart his around Patrick so as not to create to much suspicion. 

He also was not included on the List of suspects that Patrick wrote down after Lorelei made the comment about her being surprised that Red John and Patrick didn't become friends after they had shaken hands. 

For anyone curious Patrick's current suspect list is as follows:
Ellis Mars
Dean Harken
Jason Cooper
Walter Mashburn
Vint Molinari
Dr. Linus Wagner
Virgil Minnelli (who is my second choice personally for being Red John as he also fits all the other pieces)
Dr. Towlen Morning
Osvaldo Ardiles

That being said clearly Steiner is not present on this list which gives him a perfect cover but only time will tell. 

The biggest thing that led me to Steiner however was in season 3 during the episode in which he dies. After he makes the phone call about having the body him and Jane start talking. Steiner brings up Lisbon and asks Jane if they will let her in on the secret. Jane tells him in time, which (I don't remember the exact phrase of the comments) Steiner makes another remark and then makes this comment:

"She reminds me of... well never mind"

No further comments happen after that. 

It may be considered a stretch, but since it happens as a passing comment and is never brought back up, I think it's fair to say that it as a slip of the tongue with a reference to Jane's wife. I understand the Red John would have never really have met Jane's wife, but I think that there is a possibility that this is true, especially considering some other comments about Jane and Lisbon in recent episodes. For instance Lorelei's 

"I think you're just a little bit in love with Theresa Lisbon".

This is a working theory and I'm not sold on the idea, however after rewatching season 3 and seeing this episode makes me wonder. 

If all else fails here my vote is Virgil Minnelli

Good Luck Investigating