I think you misunderstand the difference between a plant and a mushroom, two discrete kingdomes. For a plant, nutrients necessary for growth are basic elements like nitrogen, phosphor, potassium, magnesium, sodium etc. in form of salts. The plants takes them from soil or fertilized water. The energy for the plant comes from the sun and the carbon from carbondioxide in the air. You can supply a plant with nutrients and it will continue growing in the same growth medium.
The mushroom however, is a composer that has to take its' energy and carbon from organic matter. It needs carbonhydrates like starch or sugar to grow. Therefore any "supplement for nutrients" would have to contain these in high quantities, making this "fertilizer" highly vulnerable for other fungi (yeast and mould) or bacteria (contaminations).
The established way to support a mushroom with new nutrients is to sterilize a growth medium and transfer a small piece of the desired mushroom in it.