The No.9 played a starring role in both of Liverpool's goals as they hold a 2-0 advantage after the first leg of the quarter-final tie.
The Brazilian laid on the assist for Naby Keita's opener before scoring himself in the 26th minute.
He is joined on the shortlist for the prize by Heung-Min Son (Tottenham Hotspur), Gerard Pique (Barcelona) and Frenkie de Jong (Ajax).
Click here to vote for Firmino before the deadline at 12pm BST on Friday.