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The former Everton midfielder is keen to banish the memories of a poor first season at Old Trafford in which he suffered from injuries, was sent off once and failed to score a goal as United finished seventh in the Premier League.
And Fellaini, who became the fourth most expensive player in United's history when David Moyes bought him from his former club Everton for 27.5 million pounds, hopes next year will go better.
Van Gaal has been linked with plenty of midfielders, including Bastian Schweinsteiger, Arturo Vidal and Kevin Strootman, but the Belgium international is not eyeing the exit.
He told Belgian reporters: "Everybody knows my club season was one to forget.
"I'm the same Marouane. United signed me one year ago. There have been some positives and some negatives, like the bad injury I picked up. Also, our team didn't quite click into place.
"But now we have a new manager -- we'll see what happens next season. In the meantime, I am concentrating on my national team.
"I am not playing here for a transfer. We'll see with the new coach, but I still feel good at United."
Fellaini, 26, scored Belgium's first World Cup goal for 12 years when he headed their equaliser in a 2-1 win against Algeria and is set to line up against Russia on Sunday