Besides Kumble, the other Indians in the top ten were Irfan Pathan and Harbhajan Singh who occupied the ninth and tenth positions respectively in the list released by ESPN-Star Sports.
In the ODI bowling ratings, Australian Glenn McGrath took the top spot followed by compatriot Brett Lee.
Among the batsmen, England's Andrew Strauss rode on his excellent form against South Africa to vault to the top of the ratings. Indian opener Virender Sehwag was placed sixth while Rahul Dravid was one rung below on eighth.
The ODI batting table was also led by an Englishman with Kevin Pietersen perched on top. The only Indian to figure in the top ten was Sachin Tendulkar at number ten.
The team rankings saw Australia continue their stay at the top in both the Test and ODI rankings. England was in second place followed by India.
In the ODI rankings, Australia were followed by Sri Lanka while India were languishing at the eighth spot ahead of only Zimbabwe and Bangladesh.