Here's what you do: you end the friendship.
You wife knows.
She's noted how your tone softens when you speak about this friend.
How your expression changes.
The little smile, the little laugh, the warmth in your eyes when you mention her.
And indeed, how often you mention her. 'Mentionitis' is what we call it.
We notice. We know. Sometimes better and before husbands know, or admit it.
Respect your wife's peace of mind.
Do not be a selfish self indulgent idiot.
Work on developing your relationship with your wife, instead. Put the effort into her that you're currently putting into your friend. Find the things in common you're finding with her in your own wife. And your bloke friends.
Because you are being very naive. Let's imagine how you'd feel if she had found a male friend she connected so well with. Not so airy innocent now, is it.