"If we continue to do well, then by the end of the year we will be there at number one," Kumble told Reuters on Thursday.
India lost the four-Test series 2-1, featuring a ill-tempered second Test in Sydney marred by poor umpiring and the hosts alleging that India spinner Harbhajan Singh had racially abused all-rounder Andrew Symonds.
The tourists won the third Test in Perth before drawing the final Test in Adelaide, which took them to second position in the International Cricket Council (ICC) rankings.
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"It is for us to take this momentum through. There is a lot of test cricket coming up now."
Anil Kumble |
The one-day team, led by Mahendra Singh Dhoni, then won the triangular series, which also included Sri Lanka, by comprehensively beating the hosts in the finals.
"It is important not to get carried away by the euphoria that has been created by the one-day series victory and also our [Test] performances in Australia. That's history now.
"It is for us to take this momentum through. There is a lot of test cricket coming up now."
Heavy schedule
India host South Africa this month for three Tests before travelling to Sri Lanka in April for Tests and one-dayers, while the Australia and England Test sides are also scheduled to tour India later this year.
Kumble said the resilience and unity his team displayed during the controversies in Australia had convinced him India had the potential to become world beaters.
"In Australia when things were down, or when things were tough, it was important for all these players to get together and ensure they were a lot more resilient and come back stronger.
"We did that in Perth and also in Adelaide and then the one-day series. It filtered down and rubbed off on the one-day squad as well and (led to) brilliant performances by them."
Kumble aims to cap his career by leaving India at the very least within touching distance of the top.
"I'd definitely like to create that kind of environment where we can reach that level, if not get there when I am there.
"It is important that we develop that kind of a strategy and momentum and ensure that we get there.
"We definitely have the quality and potential to get to number one. Although we are number two, in terms of points we are way behind (Australia)."