Henderson, 24, has only played once all season and is open to embarking on a six-month or 18-month loan in the new year. Dutch sources have confirmed Ajax's interest and the club enquired about Henderson 18 months ago when his season-long loan with Sheffield United ended.
United have not decided whether to let Henderson go on loan in January and he is expected to start in the final Champions League group stage match against Young Boys at Old Trafford on Wednesday night. Henderson is believed to be eager to impress Rangnick.
The Ajax chief executive and former United goalkeeper Edwin van der Sar is a confirmed admirer of Henderson and the Dutch champions could cash in on incumbent number one Andre Onana in the New Year. Onana, 25, has played once since January due to a doping ban and is out of contract in June.
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