According to Polish website Sportowe Fakty, Leicester have agreed to pay £7.4m for Kapustka.
The 19-year-old is expected to undergo medical examinations today, and has agreed a long term contract with the Premier League champions.
Kapustka will become the most expensive transfer in the history of Polish league, after Adrian Mierzejewski signed for Trabzonspor in 2011 for £4.5m.
The Polish website say Kapustka has made a very good impression on Claudio Ranieri, who also asked for advice on the player from Polish Football Association’s president, Zbigniew Bonie, and the Italian received a positive feeback.
The left-winger scored five goals and got 10 assists for Cracovia Krakow last season in 35 appearances, and was impressive at Euro 2016 in France.