Woolston was released by Newcastle, partly because he stands at around six feet tall.
The Manchester Evening News reports that United have taken the 20-year-old goalkeeper on trial.
The youngster was on the bench for the Manchester Untied Under-23s’ 2-0 win at Middlesbrough on Sunday.
United are keen to bring in a new goalkeeper to provide competition for Matej Kovar and Alex Fojticek.
