Chelsea suffered fresh frustration after blowing the lead in a 1-1 draw against Crystal Palace, while Newcastle beat Tottenham 2-1 on Sunday.
Manchester United will also notably play at home to 2022 Europa League runners-up Rangers and go to Portugal to play Porto, another of Jose Mourinho's old sides.
Ex-Liverpool manager Jurgen Klopp had only won two of his 11 away games against Manchester United.
Manchester United crashed to a last-gasp 2-1 defeat against Brighton and an Erling Haaland's hat-trick fired Premier League champions Manchester City to a 4-1 win against Ipswich on Saturday.
Arsenal's two defeats to Villa last season cost them the chance of a first league title in 20 years.
Maddison, whose form tailed off for Tottenham following a strong start to the Premier League season, is among seven players who will not be on the plane to Germany.
The win takes Pep Guardiola's team two points clear of Arsenal at the top of the table after 37 games.
Manchester City closed in on a fourth consecutive Premier League title by thrashing Fulham 4-0 on Saturday, while Burnley were relegated from the top flight after a 2-1 defeat at Tottenham.
Fifth-placed Tottenham's third successive defeat leaves them seven points behind fourth-placed Aston Villa.
Arsenal held on for a pulsating 3-2 win over arch rivals Tottenham in the north London derby to keep their grip on top spot in the Premier League.
Liverpool were held to a damaging 2-2 draw by Manchester United as they handed the initiative to Arsenal in the Premier League title race
Tottenham missed the chance to move into the Premier League's top four after a 1-1 draw at West Ham, while Newcastle were also held 1-1 by Everton on Tuesday.
Spurs have now come from behind to win in four of their last five home games and needed another second-half turnaround after Tahith Chong's strike put Luton into a shock lead after just three minutes.
Tottenham wasted a chance to move into the Premier League's top four as they slumped to a shock 3-0 defeat at Fulham
Injury-hit Liverpool moved four points clear at the top of the Premier League with a 1-0 win at Nottingham Forest, while Tottenham beat Crystal Palace.
Premier League strugglers Everton salvaged a 2-2 draw with Tottenham thanks to Jarrad Branthwaite's last-gasp equaliser, while Aston Villa moved into fourth place with a 5-0 demolition of Sheffield United on Saturday
Liverpool sit five points clear of second-placed City, who have a game in hand as they try to spoil Juregen Klopp's bid to bow out with the second Premier League title of his nine-year reign.
Manchester City had lost all five of their previous visits to Tottenham's plush arena without scoring a goal since the stadium opened in April 2019