The paper claims the club's board have grown increasingly frustrated with United's displays and are demanding a huge improvement - starting with the game against Olympiakos.
The Daily Telegraph says Moyes' future lays in the hands of the club's supporters who have continued to display the patience demanded of them by Sir Alex Ferguson on his departure from Old Trafford last year.
Moyes has urged the fans to get behind the team again on Wednesday and told the club's official website: "The players are capable of turning it around. We're all desperate to put things right and make sure we play better to give the supporters here something to shout about.
"They shouted [against Liverpool] and we didn't give them anything on the field. When we went to Greece, the Olympiakos fans played their part so hopefully our fans will roar us on.
"We have to go for the throat to get the win. We won't be gung-ho but we will certainly go with a mindset to overhaul the deficit as quickly as we can.
"We won't be reckless as we could find ourselves with a bigger mountain to climb but we can be forceful. We have to be if we're to keep ourselves in the Champions League."