The 31-year-old midfielder's deal is due to expire at the end of the season, leaving him free to discuss a move elsewhere.
But Meulensteen is confident that the former Chelsea, Reading and Aston Villa midfielder will agree terms to extend his stay at the London club.
"I know that they're still in talks," he said. "It's clear that Steve would love to stay here.
"He's doing very well here so I hope we come to a suitable solution."
Sidwell has spent the past three years at Fulham, having originally agreed a six-month deal in January 2011.
The combative midfielder has been one of the standout performers for the Premier League strugglers this season, scoring five goals in 22 top-flight appearances.
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