England has been ranked No.1 in the world since last August but, with the first Test of the summer beginning at Lord's on Thursday, Anderson insists the team want more.
"We don't just want to stay No.1 in the world. That's not what is driving us on. We actually do believe that we can become one of the best, if not the best, England teams there ever has been," The Daily Star quoted Anderson, as saying.
"Once we finish playing we want to look back on something we can be really proud of. We want to create a legacy. We want to be a team that people look back on and think, 'That was a great team' - a group that young kids look at and think, 'We want to be in a team as good as that'," he added.
England had a below par winter, losing all three Tests against Pakistan in the United Arab Emirates and drawing the two-match series in Sri Lanka.
After three Tests against the West Indies, South Africa will tour in July for three more before England travel to India having not won a Test series there since 1984-85.
"Our goal for a long time was to be number one in the world. Once we got there we wanted something else to inspire us and help us improve as a team," Anderson said.
"We want to win everything we can. Going to India is going to be a big task because it's somewhere where we haven't been successful in the past," he added.
