Set ADC input to high impedance
You have two options:


Use high impedance and low drift OP AMP
Use MOSFET switch to disconnect LED from ADC input


The feasibility of each approach depends on your timing requirements, actual voltages to measure etc. You have to tell us more about your task to get reasonable answer.

Both methods require medium price (several USD) components to work properly, you can not do on cheap garbage once. I do not see any option to use BJT.

For the first method, you can use OPA365 (TI, 5V supply) or AD8655 (also 5V).

For the second method, I strongly advise using CMOS switch ICs. ADG721 (.2, .3) are very good. You have to connect negative pin of your LED to GND and to connect "channel" of the switch between positive pin of the LED and ADC input.

However, I do not understand why not to use more common solutions like Light Sensitive Diode and transconductance amplifier.

I can provide more information if you are interested. Pls answer my questions.