Lazio sold Kozak to Villa on deadline day and he had no time to visit the club after being called away with the Czech Republic squad.
"I must say I will miss Rome. Lazio gave me my chance in big time football and I must thank them for that," he said.
"I have already spoken with Lambert, but only time will tell what my role will be: I definitely want to make the most of this chance, playing in the Premier League is my dream."
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