West Ham endured a terrible start to the current Premier League campaign and there were widespread rumours that the club hierarchy could potentially sack popular manager Bilic due to the poor run of form.
However, the Hammers have enjoyed a dramatic upturn in fortunes over the past few months and it has been claimed that Bilic will be allow to continue in his post as manager at the London Stadium if he is able to guide the Hammers to a higher finish than ninth.
West Ham currently sits ninth after 24 matches, five points behind eighth-placed West Bromwich Albion, who they host on Saturday.
A London Stadium source said: "There's nothing we want more than for Slaven to go onto his third year with us but we really do need to start seeing some decent performances.
"There have been some scrappy wins and we need to see some good football and stuff to please the fans. That's important.
"Then we can go into next season free of any source of anxiety and think about another contract at the end of this one as has always been the case at this club. That was what we wanted to see and it was great to watch.
"It's West Brom next and they are a good team but we have real confidence and if we continue like that a top eight finish is on."