Lazio and Sparta have been drawn against each other in the last 16 of the prestigious European club competition.
Kozak, who has been on the books of Villa since the summer of 2013, has backed his former club Lazio to win the tie.
Despite being from the Czech Republic, the 26-year-old striker has suggested on Twitter that he will not cheer for Sparta.
Villa are at the foot of the Premier League table at the moment with just 16 points from 26 matches.
The Villans are as many as eight points behind 17th-placed Norwich City and are in real danger of going down to the Championship at the end of the season.
Remi Garde’s side will return to action on Saturday afternoon when they take on Stoke City away from home at the Britannia Stadium in the Premier League.