The Red Devils have been linked with a move for the Portuguese star since last summer's transfer window and recent reports have suggested that Moyes was looking to make a move for the player this month.
It has been suggested that the Red Devils can only have the Real Madrid ace on loan this month if they pay £20m for the star's services in the summer.
However, it now appears that the Manchester United boss is having doubts over the potential signing of the Portuguese international.
The Manchester United boss has been on the look out for a new left-back since arriving at the club before the start of this season and, with Patrice Evra ageing, the Red Devils manager appears desperate to bring in a long-term replacement for the left-back.
However he may now have to look elsewhere as he doesn't seem completely happy with Coentrao.