The Bayer Leverkusen recruit only joined the club in the January transfer window after they guaranteed him first-team football.
Chelsea were one of a number of clubs, thought to include Borussia Dortmund and Bayern Munich, who competed for his signature with Bayer Leverkusen.
The talented winger had impressed for Wolfsburg's under-19 team and with the Germany youth side.
And United scouts were left impressed again when they travelled to Leverkusen to watch him in action earlier this month.
The report claims Moyes's willingness to use young players in the first-team could swing it United's way, with Januzaj an example of the kind of playing time Brandt could expect at Old Trafford.
Chelsea remain very keen on the Germany youth international, who is regarded as one of his country's top young players.
Mourinho's side have clearly targeted signing the best young players in the world in recent transfer windows and Brandt would certainly fit that bill.
But his path to the first-team would be blocked by several high-profile names, not least Eden Hazard, Oscar and Willian.