Brendan Rodgers's team, third in Group B with three points from two matches, have not yet shown the swagger that swept them to second place in the Premier League last season and they laboured to a 3-2 win at bottom club Queens Park Rangers on Sunday.
Liverpool, though, have won all three previous games against Real in Europe's elite competition and manager Rodgers is confident his players will give the 10-times champions a run for their money in front of a typically raucous home crowd.
"Real are playing as well as they have played for the last five to 10 years," he told the club website (www.liverpoolfc.com).
"What's great for us is that we're playing at home. We have a great crowd and this is a team that can rise to the level.
"Real Madrid, as the champions, are an exceptionally good side but we'll be ready."
Liverpool's shortcomings were all too evident against QPR and with striker Daniel Sturridge missing with a calf injury and Mario Balotelli short of confidence, breaking down Carlo Ancelotti's side could be a problem.
Real have no such issues up front and with Cristiano Ronaldo bagging 15 goals in eight La Liga matches, Rodgers is well aware of the challenges Liverpool face.
"He is an amazing player and his evolution over the past few years into becoming a goal-scorer has been incredible," said the former Swansea City boss.
"Real have everything, a lot of experience, top players, speed and technique."
Ancelotti's men have hit form in La Liga with five straight victories but they look likely to be without forward Gareth Bale who has a buttock muscle strain.
Defender Alvaro Arbeloa, who spent two and a half seasons with Liverpool, is looking forward to returning to his former club.
"It will be a great experience for me but I have also told my team mates to enjoy the match at Anfield as much as possible," the Spaniard told reporters.
"We will face a team that will go out and fight to the death and give everything because they need to win."
Real top Group B having already beaten Swiss club Basel and Ludogorets of Bulgaria.
"We are doing very well and are on track," Arbeloa said. "We know we have two games against Liverpool now which will be decisive in where we finish in the group."