Medel, 28, has had one spell in the Premier League already, but suffered immediate relegation with Cardiff City during the 2013/14 season.
Last summer, Medel moved on to Italy with Inter Milan, playing 44 games for the club after a strong World Cup with Chile, and he is now seen as an important player under Roberto Mancini, having again impressed on the international stage at Copa America this summer.
Inter have overhauled their squad though, and Calcio Mercato report that West Ham were hoping to take advantage of that by targeting a move for Medel ahead of the January transfer window.
However, it's also stated that Inter Milan want to extend Medel's contract by another year in a bid to fend off interest from the Hammers, with Mancini keen to keep him at the club.
Capable of playing at centre back and in defensive midfield, Medel's nickname of 'The Chilean Pitbull' is well deserved, as he is a physical, aggressive enforcer who loves to break down play in front of the back four - something he has done for club and country with great success.
A move to West Ham would be a surprise though, considering that the Hammers snapped up midfielders Pedro Obiang and Alex Song over the summer, and whilst he may want another crack at the Premier League, it would be a shock to see him snub a new deal at the San Siro for Upton Park.