The 19-year-old is wanted by a number of clubs including Everton, Southampton and Borussia Dortmund.
'Sportsmail' reported that Leicester made an offer of £6.25m at the weekend which was rejected, but now Cracovia are seriously considering the Premier League champions' improved offer.
The winger has made 65 appearances for his current club, scoring eight goals and making 12 assists.
Kapustka also has 11 caps for Poland and has scored two international goals.