The Englishman was a target for Arsenal and Real Madrid but boss Louis van Gaal is determined to bring the 20-year-old to Old Trafford if Angel Di Maria leaves the club.
The Red Devils were facing tough competition for the 24-year-old midfielder as well after it was announced last week that he was ready to leave Borussia Dortmund to join Bayern Munich.
But according to Metro, United are in pole position to sign the German who is believed to have agreed terms with the club on a move.
Last week, the midfielder confirmed that he could leave Die Borussen during the summer transfer window.
"We are holding talks yes, but no decision has been made. I can't say more than that on this," he said.
"I'll leave it open as to whether they continue without me. BVB are a great team and a really good coach is coming.
"I don't know how the team will look next season, the challenge will be to get the great potential of this team back on the pitch. We managed to do that too little during the last year."