The former Chelsea and Reading midfielder, whose current deal expires at the end of the season, was recently offered a 12-month extension by the club.
But, although his representative Eric Walters confirmed that he turned it down, he insists it was because the 30-year-old wants to commit to the club for two years.
Walters told West London Sport: "Steve wants to stay at Fulham - he hasn't got it in his mind to go elsewhere.
"The club recently made an offer of a one-year contract extension but in mine and Steve's opinion he is worth at least two years.
"He is in his prime physically, he's always likely to nick you a goal or two and he does his talking on the pitch.
"Anyone that has been watching Fulham play this season I'm sure will agree that Steve has been among their most consistent performers.
"We'll wait and see what transpires over the next few months before we make any firm decisions regarding his future."