The Cottagers have won three of their nine Premier League games since Meulensteen replaced Martin Jol at the start of December, climbing out of the relegation zone in the process.
Christensen made his Fulham debut in the recent FA Cup 1-1 draw at Norwich, coming on as a second-half substitute, but his current deal is due to expire at the end of the season.
The Denmark Under-21 international joined Fulham in 2012 and says that Meulensteen has had a positive influence on the club, particularly its younger players, since taking the job.
"It was tough when Meulensteen was appointed," he told Ekstra Bladet.
"But we have won some matches and right now, we are out of the relegation zone. But it is a tough league where all teams can beat each other.
"Rene Meulensteen is a very knowledgeable manager with some nice ideas.
"I feel he has been very good at integrating many young players at the first team training sessions.
"We have four or five young talents who are training with the regulars. It shows he has confidence in us."
Speaking of making his Fulham bow, Christensen added: "It was fantastic to get my debut in the oldest and most prestigious cup tournament in the world."