The 27-year-old Czech striker has only made two substitute appearances for the club this season and is entering the final six months of his contract.
Kozak, 27, joined Villa from Lazio in September 2013 for €6.5 million [£5.4 million] but suffered a career-threatening leg break during a training session midway through his first season in England which ruled him out of first-team training for over 18 months.
The Czech forward, who scored four goals in 15 games before being sidelined, eventually made his playing comeback for the senior side early last season in the League Cup before going on to earn four Premier League appearances over the course of January, but he failed to feature for the rest of the 2015-16 campaign after breaking his ankle in the 0-0 draw at West Bromwich Albion.
Despite fully recovering in time for preseason, he has still only made two appearances off the bench so far this term, and with Villa boss Steve Bruce recently revealing that he is free to find a new club in the New Year, the seven-times capped international accepts that the time has come for him to seek out a fresh start elsewhere.
“I understand, I was injured a lot so it was not easy for coaches to see me in training, and even after the second surgery the ankle problems took a long time to go away so the chances to impress with the other strikers haven’t been available enough. That’s why I want to restart my career somewhere else.
"Either I leave now or in the summer, when my contract expires and I'll be a free agent,” Kozak continued. “But I think that Aston Villa would not have a problem with me leaving now. Having not shown much over the last three years, it is clear that no large fee for the eventual transfer would probably be needed.”
Where Kozak heads next now remains to be seen, but he would be open to joining another English club if he received the right offer.
The towering front man, who began his career with Czech second division side SFC Opava, has not ruled out moving back to his homeland either after spending part of the summer training with his old club, but a return to Italy would be his first option at the moment.
“We'll see what opportunities arise,” he added. “I will not hide that I would definitely not resist returning to Italy. I know the country, I have many friends there and I lived there for a good time, but if interesting offer from England appears, why not stay here?
“I never want to rule out anything, but my priority now after all I’ve been through is more abroad. As I mentioned, I would most probably be drawn back to Italy."