The Light Blues will be looking to book their place in February’s final as they take to Hampden on Sunday afternoon and Tavernier says the squad are ready to give everything to take that next step.
Speaking to the media at this afternoon’s pre-match press conference at the National Stadium, Tavernier said: "We are really looking forward to it, we have had a good week of training so we are well prepared for the game in hand.
"We won the Scottish cup last season and there's a lot of experience in the team but it is something that is in our sight to try and get this League Cup back to Ibrox so we will be doing everything possible at the weekend to try and get to the final.
"You want to have more days like that to share with the fans and your family but we have got an important game against Aberdeen and we have got to get past them."
Tavernier feels Rangers are continuing to improve each week under Michael Beale and says it is important they can find consistency in their performances.
Reflecting on Sunday’s Scottish Premiership victory over Dundee United, he added: "I think it is one of the best performances we have had, especially going to Dundee United. It has always been a place where the performances have not been there, but I felt we were really comfortable at the weekend and we are still working hard and still learning.
"Every day we are always improving at training and the manager is getting his tactics and messages across and we are just soaking it in. The more time we get we will improve as a team, and it is starting to show and we just have to have large spells of that in games and it will bring on the strong performances that we are looking for."
When asked about his own role in the squad, and the competition from young Adam Devine, Tavernier praised the 19-year-old for how he has stepped into the first-team environment.
He continued: "I think I have got more of a freedom in my play now to get forward, I enjoy getting forward, so it suits me well.
"Every player wants competition, you never want to be almost in cruise-control, you always want to get pushed and want more than one person in your position and Adam can play both sides and he is pushing me and Borna."