The Spain international saw a proposed deadline-day move to the Santiago Bernabeu fall through last year and has since re-established himself as United's number one, and was named man of the match in a 1-0 win away to Liverpool on Sunday.
Madrid have been hit by Fifa sanctions, which are due to take effect after the current transfer period and will prevent Zinedine Zidane's club from registering players during the next two windows, prompting suggestions they could attempt to revive their failed move for the 25-year-old this month.
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But Schneiderlin is not concerned about his team-mate's future, telling MUTV: "David is a very important player in our squad. We are very happy to have him and happy that he didn't go last summer. He is fully committed to this football club.
"When you have a player like this in goal, it's good for us because we know we are not going to concede many goals and he is going to make some saves. Well done to him."
United's win at Anfield took them back to within two points of fourth-placed Tottenham in the Premier League table.