The Red Devils attacker has been frustrated with life at Old Trafford this season, and feels he hasn't been given a proper chance to shine in the team by the former Everton coach
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United have relinquished their Premier League title and sit seventh in the table, with only a remote chance of qualifying for next season's Champions League.
Moyes' side were knocked out of this term's Champions League at the quarter-final stage by holders Bayern Munich earlier in the week, with a 4-2 aggregate defeat ending the Scot's hopes of landing a major trophy in his first season at the club.
There have been reports of unrest within the Old Trafford dressing room throughout the campaign and, according to the Sunday People, Valencia has now gone public with his discontent.
"I would like to have more minutes, I would like to have a more important role here," the British newspaper quotes the Ecuador international as saying.
"In fact, I would have liked to have more importance inside the team.
"But I have not been given the chance. I hope next season will be better for me as well as Man United."
Moyes' team currently sit nine points behind fourth-placed Everton in the race for the final Champions League qualifying place.