The 40-year-old goalkeeper says reports stating he has turned down a new deal from the club are incorrect, and he may have played his last match at Craven Cottage
The Cottagers' boss said the Australia international had turned down an offer of an extension to his current deal, but since then Schwarzer has rubbished those claims.
The 40-year-old is adamant no proposal has been made in writing and reiterated that he would need assurances of his status as the first-choice goalkeeper if he was to commit his future to west London outfit.
|7/1||Fulham are 7/1 with Paddy Power to be relegated next season
"Obviously I am out of contract and as yet I have had no official offer of a new deal contrary to reports.
"I still want to play in the Premiership and still believe I have the ability to do it. It would be nice to stay at Fulham. But the bottom line is I have to find a club that believe in my ability."
The Australian is eager to represent his nation at the 2014 World Cup, and says he needs to be regularly playing first-team football next season to earn a spot with the Socceroos.
"I still have the hunger and desire to play at the highest level and my plan is to definitely play another year. I want to go to another World Cup," he added.
"To do that I need to be playing regularly and if that means I have to go elsewhere I will go elsewhere.
"I love playing in the Premier League. I have been here for a long time and I love playing week in week out in this competition. I rate it as the best league in the world."
Schwarzer is the only foreign player in the Premier League to amass over 500 appearances.