The Daily Mail says Moyes was planning to keep Lingard to play in the Capital One Cup games but changed his mind once United were drawn against Liverpool in the third round last month.
The new United boss was already feeling the pressure following a Premier League defeat at Anfield and realised that he could not risk putting out a severely-weakened team against his rivals.
He sanctioned Lingard's loan move so the youngster could have more first-team football and Birmingham manager Lee Clark has been delighted with his progress.
"United want to review it and see how things are going," he said. "I'm hoping that David is seeing that he's enjoying his football and we're being good to him."
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