Mandzukic has scored three goals in the tournament so far, two coming in a win over the Republic of Ireland and one against Italy.
Now, with Croatia looking to make a run in the knockout phase of the tournament, Mandzukic is gaining more attention from Premier League clubs, including one in particular.
Mandzukic, who is currently playing with Wolfsburg in the Bundesliga, would be paired alongside fellow Croatian Nikica Jelavic in the Toffees attack if he makes the move.
The 26-year-old scored 12 goals in all competitions for Wolfsburg this season and has had only one season in which he has not scored in double digits in the past five years.
However, the funds for Everton may not be there unless they sell a player or two.
That may not be a hard thing to do for manager David Moyes as a few of his stars are being rumored to be on their way out of the club.
Bringing in Mandzukic will provide Everton with another attacking option up front and give Jelavic a familiar partner up front.
But, as is the concern with many players who make their way onto the international stage at a big tournament, Mandzukic is not guaranteed to match his Euro 2012 success in the Premier League.