West Ham, who are currently 14th and seven points clear of the drop zone, need two more points to reach the safety target of 40 points.
"People are talking about speculation that 38 points will be enough, but in the history of the Premier League it's always that magic number of 40," Bilic told in a news conference on Thursday.
"We are not panicking, but none of the teams, until mathematically, are safe. Maybe we have enough [points], but we can't be sure... We're three games unbeaten, and of course the confidence is higher. It's related to the way we are training and the games we play."
Bilic was not sure who will start as the goalkeeper this weekend at the bet365 Stadium. Goalkeeper Darren Randolph has featured in 22 league games but his replacement Adrian kept a clean sheet against Everton last weekend.
"I had a couple of meetings with them individually and explained my decisions," the Croatian boss added. "Darren is a great professional, of course he is disappointed but he understood my decision.
Read the full article on eurosport.co.uk: Bilic: West Ham fighting relegation fight until mathematically safe