Medel impressed for his country at the World Cup in Brazil this summer, operating in a central defensive role as opposed to his usual midfield berth.
With Cardiff having suffered relegation from the Premier League last season, they are expected to see many of their highest-earning players depart.
But with Inter reportedly offering a sum significantly below Cardiff's valuation of £10million, there is some distance between the two sides before terms can be agreed.
Cardiff are unwilling to take a financial hit on a player they signed for a fee in the region of £11m from Sevilla last summer, with chairman Mehmet Dalman setting out their position in no uncertain terms.
Dalman told walesonline: "We are not going to take a loss on a player who was a World Cup star in Brazil.
"We have made it clear what our price is and that won't change.
"We will do the right thing for Cardiff City and the player.
"There are clubs interested in him, but we have not reached agreement with anybody so far."