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The Netherlands international started Carrick's first game in charge as caretaker on Tuesday night, playing in midfield alongside Fred and Scott McTominay in the 2-0 win over Villarreal that secured qualification to the Champions League knockout stages.
It was just his second start of the season in all competitions, with Van de Beek largely an unused substitute during his time at Old Trafford.
But Carrick has hailed the 24-year-old's versatility and believes he is even capable of playing as a false nine for the Red Devils.
'We've got ideas where we think Donny's most suited but he's so flexible and adaptable, with two or three positions," Carrick told the media in a press conference ahead of the clash with Chelsea this weekend.
"He even played as a false nine for Ajax in the Champions League when they ended up getting beaten by Tottenham.
"We've got ideas for him but being flexible is a strength and a credit to what he can bring to the team."
Van de Beek came out from the cold to produce an impressive cameo performance in Ole Gunnar Solskjaer's final game in charge at Watford.
The result was a miserable 4-1 defeat but Van de Beek came up with a reminder of his quality and was on the scoresheet at Vicarage Road.
There has been talk that Van de Beek may be allowed to leave in the January transfer window, although he could well be given a new lease of life by interim boss Ralf Rangnick.
The 63-year-old is expected to sign a six-month deal with United and will have a say in the decision on who the club's next permanent manager should be after agreeing a consultant role following his stint.
Rangnick's first game at the helm is likely to be the game against Arsenal next Thursday.
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