Carrick’s side travelled to the Emirates on Sunday (January 25) having beaten Man City in their previous Premier League fixture.
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Man United were fantastic throughout and after Arsenal scored their second goal to make it 2-2, Matheus Cunha scored a screamer to make it 3-2.
Speaking to Sky Sports after the game, Carrick was asked whether he would be interested in taking over on a permanent basis.
The former midfielder didn’t give much away, however, saying: "I'm enjoying it. It's a fantastic position to be in. What happens next I'm not going to be answering it every week. I'm enjoying it and I'll continue to do what I can."