The England international suffered a terrible double leg break in Champions League action against PSV Eindhoven on Tuesday and has already undergone surgery on the problem.
The blow leaves Louis van Gaal without a specialist left-sided defender, albeit he can use the likes of Daley Blind and Marcos Rojo in the position.
However, the club are looking to address the issue when the transfer window re-opens, with Taylor reportedly an option.
A £4m offer is thought to be on United’s agenda with the Manchester giants having been monitoring the 21-year-old’s progress for some time.
Taylor has made seven appearances for the Whites in Championship action so far this term and is considered to be one of the best emerging talents at Elland Road.