Andrew Strauss's team are currently ranked number one in the world, having achieved the feat in August with victory over India.
Looking ahead, bowler Anderson has revealed that the squad are determined to create a "legacy".
"We don't just want to stay number one in the world. That's not what is driving us on," he told BBC Sport. "We actually do believe that we can become one of the best, if not the best, England team there ever has been.
"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 as good as that, we want to be in a team as good as that'."
Anderson is expected to be part of the England squad that will take on the West Indies later this month.