George was part of United's academy before becoming the first player at Everton to sign a professional contract in 2017.
The 26-year-old, who has two England caps, missed the end of last season with a hamstring injury.
The transfer window closes on Thursday.
It could be a busy end to the summer window for United as they also hope to sign OL Reign goalkeeper Phallon Tullis-Joyce.
Meanwhile, United striker Martha Thomas has had a medical at Tottenham as they look to add attacking depth following an injury to Lionesses striker Bethany England.
Everton may look to find a replacement for George should she agree a move to United before Thursday's deadline.
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