The 21-year-old joined Leeds for the start of pre-season training this month but he was omitted from the travelling party for the club’s week-long trip to the continent.
United’s squad flew out of Manchester this morning ahead of a friendly against Eintracht Frankfurt in Salzburg on Tuesday but Drury was not included and is not expected to be given a contract by Leeds.
The versatile right-back is a free agent after leaving Manchester City in the summer.
He played in the closing stages of Wednesday night’s 1-1 draw at York City, his last opportunity to catch the eye of Leeds head coach Uwe Rosler.