"It could be my last for Croatia, but let's hope it isn't as I have a feeling we can do much more here than just the quarterfinals," said the 36-year-old midfielder, referring to Friday's quarterfinal clash against Turkey.
Kovac, who has won 78 caps for Croatia and scoring 13 goals since making his national team debut against Morocco in December 1996, admitted that the last eight showdown in Vienna "is the peak of my career" as he missed the team's run to the semifinals of the 1998 World Cup through injury.
The German-born player, who has played for several Bundesliga clubs in Germany and currently with Austria's Red Bull Salzburg, has been Croatia skipper for the past four years.
After being rested for Monday's Group B game with Poland, Kovac, once a member of Hertha Berlin, Hamburger SV and Bayern Munich, is expected to resume his midfield partnership with Luka Modric against Turkey.