But the club failed to land the player and the very public row which has ensued since has been embarrassing for all involved, particularly Hammers owners David Sullivan and David Gold.
Money talks in modern day football. But such is the acrimony between West Ham and Sporting Lisbon, any hopes of resurrecting the deal seem remote.
Quality defensive midfielders don't grow on trees and the good ones cost big money.
So what are the realistic alternatives for Bilic in January, if indeed he survives as boss until then.
Brazilian Luiz Gustavo is best known for his time at Bayern Munich but excelled during a spell with Bundesliga rivals Wolfsburg. He was sold to Marseille for £9million in the summer but things have not started well for the fiery star with L'OM suffering a poor start to the season conceding nine goals in two games of late.
A bid similar to that submitted for Carvalho of around £23m could tempt the French side to sell and the 29-year-old would fit perfectly into that hole in the Hammers team. A superb reader of the game, Gustavo's biggest strength is to break up play and he has come of the best interception stats in Europe. He may be Brazilian but his qualities are destructive rather than creative, just what Bilic is looking for.
The anchor at the heart of a steadily improving Fiorentina side is Milan Badelj. As a Croatian international Bilic will be well aware of the 28-year-old's abilities. Badelj has gradually built a reputation as one of the best defensive midfielders in Serie A and indeed wider Europe.
Like Gustavo Bedelj's quality is in breaking up play but like Carvalho he also becomes a deep sitting playmaker and is known for his bursts forward quickly turning defence into attack.
At 26 Real Madrid reject Asier Illarramendi would represent the best business by West Ham if they can lure him to East London from Real Sociedad. The Spaniard was snapped up Madrid during Carlo Ancelotti's time at the club but never quite made the step up to replace Xabi Alonso.
It was one of David Moyes' first - and only - good moves to bring Asier back to Real Sociedad during his ill-fated spell as manager there because he has flourished ever since. On paper statistics show he is in the top five defensive midfielders in Europe so he won't come cheap. But he would undoubtedly be the best long term investment for the Hammers.