According to Italian media outlet TMW, the Hammers are looking to sign the 24-year-old in this summer’s transfer window as they look to bolster their squad going into next season.
The Croatian midfielder only started ten games in La Liga last season, and is looking for more frequent first team football.
Despite not having found the net on any occasion for club or country throughout the whole campaign, it is the midfielder's break up play, passing ability and precision that makes him an appealing transfer target.
The box to box midfielder is contracted at Real Madrid until June 2021, meaning the Hammer’s may have to pay big money to secure their man.
Kovacic has won the UEFA Champions League three times in as many seasons and is part of the Croatia World Cup squad that are through to the quarter finals.
Croatia will face host nation Russia in their quarter final on Saturday with a play in the final four up for grabs.