Napoli will take a two-goal advantage into their away leg against Nice, while Celtic were the other big winners in Wednesday's matches.
Celtic look destined to qualify for the Champions League after beating Astana 5-0 and manager Brendan Rodgers wants a Liverpool reunion.
Scott Sinclair scored twice at Parkhead as Celtic beat Astana 5-0 to close in on the Champions League group stage.
The transfer saga around Philippe Coutinho did not distract Liverpool as they saw off Hoffenheim but Emre Can rates his colleague highly.
Trent Alexander-Arnold was hailed by Liverpool boss Jurgen Klopp after his superb free-kick against Hoffenheim.
After their loss to Liverpool in Champions League qualifying, Hoffenheim coach Julian Nagelsmann promised resistance in the second leg.
Although Liverpool took a huge step towards the Champions League group stage with a win at Hoffenheim, Jurgen Klopp is not celebrating yet.
After scoring in Liverpool's Champions League qualifying win at Hoffenheim, Trent Alexander-Arnold described the match as a dream.
Trent Alexander-Arnold scored as Liverpool earned a fine 2-1 first-leg win at Hoffenheim in Champions League qualifying.
Napoli face a tough task against Nice despite the absences of Mario Balotelli and Wesley Sneijer, Maurizio Sarri has stressed.
After twice going close with Juventus, Leonardo Bonucci is determined to help AC Milan to a Champions League title in the next four years.
The three nominees for UEFA's Player of the Year prize are Gianluigi Buffon, Lionel Messi and Cristiano Ronaldo.
Philippe Coutinho's future has overshadowed the start of Liverpool's season, but Jordan Henderson claims the players are not distracted.
Liverpool boss Jurgen Klopp believes Hoffenheim's Julian Nagelsmann is a strong example of Germany's promising young coaches.
Ahead of Sunday's Supercoppa clash against Lazio at the Stadio Olimpico, Juventus head coach Massimiliano Allegri has fired up his team.
Jose Mourinho has tipped Manchester United to be one of seven candidates to challenge for the Premier League, won by Chelsea last season.
After watching Real Madrid outclass his Juventus side in June's Champions League final, coach Massimiliano Allegri considered resigning.
Liverpool's pursuit of Naby Keita may have been rebuffed but RB Leipzig expect more interest after the midfielder hits the Champions League.
New Nice signing Wesley Sneijder was convinced to move to Ligue 1 by the team's talent and ambition, not by watching Neymar's transfer.
Bayern Munich must compete financially with their European rivals if they are to win the Champions League, according to Stefan Effenberg.