The Dutch defender scored the winner in the 118th minute against Chelsea at Wembley last year, securing his first trophy as skipper.
The 33-year-old replaced Jordan Henderson as captain in 2023 under Jurgen Klopp and has retained the armband under new manager Arne Slot.
"If you were to lift the two trophies, I think you have a pretty good chance to be on a nice list of captains that have achieved great things in this club," Van Dijk told British media ahead of the final against Newcastle.
"That’s obviously a big dream of mine since I became the captain of the club. We’re not there, we have a lot of hard work still to do.
Van Dijk's contract expires in June but he says he has not been fazed by the uncertainty over an extension.
"I feel I am in one of the best shapes in my career and you have been seeing that," he said.
"I enjoy playing, I enjoy leading the boys out, I enjoy being there for each and every one of them and I enjoy the responsibility more than ever, maybe because I am getting older slowly. So let’s wait and see."