The 31-year-old, who comes to the end of his contract in the summer, is believed to have been offered a 12-month extension by the club.
However, reports have claimed that Sidwell is seeking a two-year deal at the club due to his contributions so far this season.
"I know he would love to stay here," talkSPORT quotes Meulensteen as saying. "He definitely gets the credit he deserves from us and that is the most important thing.
"His fellow teammates respect him tremendously and myself and the staff respect him tremendously for the player he is and what he does for us."
Sidwell, who has netted five goals so far in the campaign, joined Fulham from Aston Villa in 2011.