I think what you are trying to say is that you want to find an independent instructor and set a fixed price with him, and then rent an aircraft from an FBO to do your training in with that CFI.
While there may be an FBO that would allow it, most will probably not. First reason would be insurance. You are not a pilot, so you can't rent a plane, so you would have to ask this instructor to rent the plane for you. Then the instructor would have to assume any liability personally if you bent or broke the plane while being taught. I don't think either party would be comfortable with that.
Also, if the FBO employs their own CFI, they would be taking business away from him/her in the process.
You may find an independant CFI who will work with you privately on ground school at a more resonable rate. I have done this for a few students who needed extra help.
Good luck with your training