The 22-year-old won the young player of the season award after showing rapid improvement following the arrival of Klopp in October, going on to earn a spot in Germany's European Championship squad in France.
Having started in the 2-0 Euro 2016 semifinal defeat to the hosts last month, Can believes he has all the attributes to become a key member of the Liverpool squad.
"I now have more experience and have played in international games," Can told the club website.
"I was one of the new players when I came here two years ago and now I want to lead the team, I want to give my best for the team," he added.
"I want to go my own way as Emre Can. Of course, my target is to become a legend one day."
Can has revealed that his strong relationship with compatriot Klopp had been a key factor in his improvement after an unconvincing start to his career on Merseyside.
"For me, it's very important to have the trust of the manager, and I have his trust," Can added. "That's why I can always show my best."
Despite his confident expectations for the season ahead, Can downplayed comparisons with Liverpool's former talismanic captain Steven Gerrard.
"That's of course a big, big honour," Can told reporters on Wednesday. "But I say I have lot of respect for him and I am far off that level he played for Liverpool."