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.