Serial Champions League winners Real Madrid bared their fangs but left Munich staring down the barrel of a second consecutive season without a major trophy with coach Alvaro Arbeloa's tenure looking tenuous.
Thomas Tuchel says he now has more "clarity" after England's final home match before the World Cup, but there appear to be more questions than answers after a limp 1-0 defeat against Japan.
Alexander-Arnold's chances of selection for the tournament in north America appear slim as he not only missed out on the initial squad, but was also overlooked in favour of Arsenal's Ben White after Jarrell Quansah dropped out due to injury.
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Vinicius Junior won and converted two penalties as Real Madrid thumped Real Sociedad 4-1 on Saturday to move provisionally top of La Liga.
Real Madrid twice came back from behind to draw 2-2 against Elche in La Liga.
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Trent Alexander-Arnold will receive a hearty welcome from Liverpool manager Arne Slot when he returns to Anfield with Real Madrid on Tuesday.
Trent Alexander-Arnold was left out by England for its upcoming World Cup qualifiers in the national team's first squad announcement since the right back left Liverpool to join Real Madrid.
Kylian Mbappe struck from the penalty spot as Real Madrid beat a dogged Osasuna 1-0 on Wednesday to make a winning start in La Liga under new coach Xabi Alonso.