The Reds' second-place finish in last season's Premier League sees them back in Europe's premier competition for the first time since they were knocked out of the group stages back in 2009.
The creative Coutinho was vital to the Reds' ultimately unsuccessful title challenge last term, carving out seven assists and five goals as Brendan Rodgers' side finished two points behind champions Manchester City.
Coutinho, who arrived from Inter Milan for around £8.5 million in January 2013, will have an added responsibility placed on his shoulders in the coming season following the loss of Luis Suarez to Barcelona.
Rodgers has brought in additional cover in the attacking areas with the likes of Adam Lallana, Rickie Lambert and Lazar Markovic joining the club in the summer, but the Northern Irishman believes it is the current number 10 who will dazzle - and he threw down the gauntlet for the Brazilian to do it in the upcoming European campaign.
Speaking to reporters after watching his side beat Borussia Dortmund 4-0 in their final pre-season warm-up, Rodgers said: "He's so gifted as a player. He's just magical. His ability to get out of tight situations and his view of the game is incredible.
"He's come into this country and league, and lit it up with his quality. It's now about doing that on the big stage - the Champions League, and he's got the chance to go and do that.
"I think that even at that level, he will show what great qualities he has. I really see him over the next four or five years, being a big force in world football, both for Brazil and Liverpool.
"He's an incredible operator, just magical to watch and he's the kind of player that supporters come to see. We're very glad to have him. And that's his best position - playing between the lines, he doesn't get marked. He drops to the back of midfield, he draws defenders out, and the weight of his passes is phenomenal.
"He was outstanding, and what he's added to his game is that relentless pressing. He's very strong under pressure on the ball, and puts pressure on the opposition when he's not on the ball."
Coutinho played a starring role as the Reds saw off the threat of BVB at Anfield, as he scored the third goal and created the opener for Daniel Sturridge with a deft through ball on 10 minutes.
Dejan Lovren marked his home debut with a goal on 14 minutes, before Jordan Henderson capped off the win just after the hour mark, following Coutinho's effort five minutes after the restart.
The Reds begin their Premier League campaign with a visit of Southampton on August 17.