The Czech centre forward was wanted by the St Andrews club, but an offer was reportedly refused.
The Czech Republic international has had a torrid time in the Midlands since moving to Villa Park from Lazio in 2013, with prolonged periods on the sidelines due to injury and poor form.
Despite Remi Garde replacing Tim Sherwood as the club’s manager, Kozak still remains a player out of the first-team thinking.
The lofty striker has scored four league goals in 14 appearances for the club in the last two years, with a broken leg blighting the eastern European’s career.
Garde has stated that no players were allowed to leave in the loan window, but that there was scope for potential departures in January.
“No players left as I have got players struggling to be fit,” The Mirror quote the Frenchman as saying.
“I decided that nobody would leave, but maybe they will in the next window.”
The likes of Jordan Ayew, Scott Sinclair and Gabby Agbonlahor are ahead of Kozak in Garde’s selection preferences currently.