The 45-year-old former world number one suffered compound fractures in his right leg.
Rangnick is expected to be installed this week as United boss until the end of the season.
The 63-year-old Rangnick is currently head of sports and development at Russian club Lokomotiv Moscow.
Although the results have been spotty, James said the Lakers "have been playing better of late."
The Women's Tennis Association threatened to end its lucrative business in China unless it was assured of her safety.
