Jose Mourinho is looking to sign a new left-back before the summer transfer window slams shut and Max is eager to move to Old Trafford.
A reported source close to the 24-year-old told CalcioInsider: “He is keen to move up in the career, he loves the Premier League and is ready to join Manchester United – his favourite club.
“Philipp is the best (left back in Germany) and at his peak now, Augsburg would want around €40m.”
Max is under contract at Augsburg, who finished 12th in the Bundesliga, until 2022.
He recorded 13 assists in 33 league appearances last term but was omitted from Joachim Low’s Germany squad for the World Cup in Russia.
Cologne left-back Jonas Hector was picked instead the source told CalcioInsider: “He was disappointed as he deserved to go to the World Cup.
“I’m not certain why the manager prefers Jonas.”
Ashley Young occupied the left-back spot at Old Trafford the majority of last season, despite it not being his natural position.
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The 32-year-old edged out Luke Shaw, who has never won over Mourinho and could be sold to make room for a new arrival.
Mourinho is eager to quickly get his transfer business done in this window.
Portuguese right-back Diogo Dalot has been captured from Porto on a five-year deal while an agreement is in place to sign Shakhtar Donetsk midfielder Fred.