Having taken charge after the dismissal of Ruben Amorim in January, Carrick signed a deal with United to the end of the season.
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Since then, Carrick has guided United to third place on the Premier League table, with support growing that he be given the job over the long-term.
TalkSPORT says United chiefs are giving Carrick every chance to convince them to extend his stay by deciding NOT to begin interviews with other candidates.
As it stands, United have not made contact with anyother options, so suggesting that there is a preference that it is now Carrick's job to lose.