The Czech was heavily linked with the Scottish champions.
The striker had starred in the Europa League with Lazio and it was hoped he could be a regular goalscorer in English football.
But he broke his leg early on and has struggled to establish himself ever since. This summer Aston Villa moved for strikers in the transfer market this summer. The club brought in Jordan Ayew and Rudy Gestede in the summer and Kozak spent much of the season watching from the sidelines.
A couple of months ago he was scouted by Celtic ahead of a potential January move after impressing for Aston Villa's under-21s. Celtic boss Ronny Deila saw him score twice in an under-21 tie with Derby County, as reported by the BBC.
But he never made the move to Celtic as Remi Garde brought him back into the first-team fold.
At the same time he was also linked with Italian side Genoa and he told Czech paper Denik this week about that interest:
"Of course, the possibility here was pretty fair.
"As I said at Aston Villa, I was not part of the team, so I was looking for another engagement. I am glad that the interest manifested from clubs like Genoa and Celtic.
"For me it is now important to play and wrestle a place in the starting line-up. I was a long time without football, without matches and everything that goes with it.
"Therefore, now I enjoy the burden of fighting. So if the chances of Aston Villa continue, I just like it."
Celtic were of course on the hunt for a striker at the time and Kozak was not a part of Villa's plans. But his work-rate has impressed Garde and he has finally become a first-team fixture at Villa Park - so no Celtic deal currently looks likely.
But he was clearly flattered by the idea and who knows, maybe one day he will end up at Villa Park.