The Cottagers are currently in 10th place in the table, nine points above of the relegation zone with six games left, and Schwarzer has revealed that he and his teammates want to show that the club deserve their league position this season.
The 40-year-old told the club's official website: "We've got one more game than most teams as we're playing Chelsea on Wednesday.
"So we've got six games remaining and the target will be to try and get to that point where we are mathematically safe and then we'll try and finish as high as possible in the table.
"There are points available and it's good for momentum for next season if we can prove to people that Fulham deserve to be in the top half of the table."
The former Middlesbrough goalkeeper has yet to sign a new contract at Craven Cottage.