The Hammers could have sacked Bilic at the end of last season, but they instead chose to give him the final year of his contract, backing him with signings such as Joe Hart, Pablo Zabaleta, Javier Hernandez and Marko Arnautovic.
However, Bilic has picked up just four points from the first six games of the season, losing the first three of the campaign and also losing 3-2 to London rivals Tottenham Hotspur on Saturday afternoon.
That defeat has piled the pressure back on manager Bilic ahead of this weekend's huge clash with Swansea City, with rumours suggesting that the Hammers are already looking at possible replacements for Bilic.
Now, The Mirror claim that West Ham did sound out German boss Thomas Tuchel for the role, but the former Borussia Dortmund man isn't interested in the job.
Tuchel, 44, replaced Jurgen Klopp as Dortmund boss in 2015, and won 63% of his games in charge of the Bundesliga giants, before parting ways at the end of last season.
Widely recognised as the most impressive manager without a club right now, Tuchel will be in demand whenever a job does become available, and West Ham allegedly looked to steal a march on their rivals by asking him whether he would be interested in succeeding Bilic, if results don't improve.
However, Tuchel isn't interested in the job, meaning that the Hammers must either stick with Bilic or search for another target, as the managerial position at the London Stadium become a hot topic.