In his time out, Rose courted controversy when criticising Spurs' transfer dealings - challenging the club to sign players he did not "have to Google".
But manager Mauricio Pochettino is happy to sweep that episode under the carpet as he prepares to take on Jurgen Klopp's men at Wembley.
The Spurs boss said: "He is happy, his behaviour is fantastic. You could see he helped the team in the final few minutes against Real Madrid.
"His mind is clear that what happened is in the past and we need to move on. He is part of my plans. The past is in the past.
"In life they are young and they can [make] mistakes but the most important thing is that they can learn from that. Fans want the best for the team and Danny is our player.
"Our fans are fantastic and they show good love and that they care for our players. He has four years left on his contract."
Pochettino added on Rose's condition: "He is not ready to start because he still needs to build up his fitness. But we are so happy because he is doing very well and the possibility to be on the bench on Tuesday was important for the team.
"To feel like you are involved again is so important after 10 months out. Now it's the process to build up and try to get better every day.
"Then we will see on Wednesday if there is a possibility for him to be in the starting XI [against West Ham in the League Cup]."
Pochettino will have to make do without Mousa Dembele and Victor Wanyama against Liverpool - the Belgian suffering a setback in his return from a hip injury - but Ben Davies and Georges-Kevin N'Koudou are back in training.