The 32-year-old, who moved to Craven Cottage in August 2011 but injured his cruciate ligament last November, saw his deal expire with Martin Jol's side in the summer but the Fulham boss has admitted he would be willing to offer the Czech defender a new contract if he can prove his fitness.
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"Grygera has had a setback because he got injured. He looked ever so well, played in the reserves and kept them together and they had better results than before," Jol told the Fulham Chronicle.
"He has a thigh problem so we have to wait and see because we wanted to make a decision on him in the next week and now there's a little step back again."
The Czech Republic international has made only seven appearances for the London outfit.