Sorry, I was wrong about the hearth of the fireplace. I checked and found this:

3. ALL FIREPLACES SHOULD HAVE A NONCOMBUSTIBLE HEARTH EXTENSION

All fireplaces must have a noncombustible hearth that extends 20” beyond the front of the firebox and 8” to either side. Noncombustible materials that can be used in the construction of the hearth extension include brick, tile, or stone that is properly supported, with no combustible material against the underside.

Also take care to ensure that combustibles are not placed less than 28 inches from where the sidewall opens (again, specific model requirements vary, so consult installation manuals).

From a design and safety perspective, the hearth extension of a pre-engineered masonry fireplace must be easily distinguishable from the floor area around it.

Never mind, thank you.

Hi JIMMIEM, do you have further suggestion after my answers to your question, thank you.

If you want to use attach to the concrete check out Sika AcouBond System.
Is this a new room...was there ever carpeting on the exposed subfloor? Where does the room go? You could bring the concrete up to the level of the current wood subfloor and then add another layer of plywood on top of everything. Depending on where the room goes you could use a transition to a lower floor surface. Or just take the concrete down about 1 /4" and attach a piece of 1/4" plywood to the concrete and glue the hardwood to the plywood in that area.
What direction will you be installing the hardwood? What species is the hardwood?

This is an old house I just bought, there used to have carpet on top of the floor which covered all concrete and wood subfloor. I am now changing carpet to solid hardwood floor (Brazilian Oak). Your suggestion to add plywood or cut concrete sounds the ultimate solution, but it might need too much work. I am now planning to grinder the concrete to the level with subfloor, and undercut the hearth, then I will install hardwood and keep the small concrete area floating only with wood glue between the piececs. I checked that area, only 3 or 4 short pieces need glue, others can be fastend through the other side of the planks nailed down to the wood subfloor. Since that's the corner area, not much traffic I hope this would be fine. How do you think? Any potential problems I missed? Thank you.

Good plan. Keep end joints to a minimum in the concrete area to minimize movement (squeaks).

Okay, thank you very much.

One more thing. The fireplace is a focal point of the room so spend a lot of time planning the hardwood layout around it so that you don't wind up with thin or short pieces around it. Also, the flooring will look best if the boards don't look angled around the fireplace.