According to the Mirror, United's 1-0 loss to Newcastle at Old Trafford saw them suffer back-to-back home defeats for the first time since 2002.
Moyes is under huge pressure with United out of the title race and facing a fight to qualify for the Champions League with a top-four finish, the report said.
However, the United boss said he is unlikely to go on a huge spending spree in January, despite his squad needing drastic improvement, the report added.
He said that he would not be under pressure during the January transfer window as he would try to do only the right things.
Everton and England left-back Leighton Baines remains United's only realistic target when the transfer window re-opens on January 1, the report further said.
Image: David Moyes
Photograph: Mark Metcalfe/Getty Images
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