A vulcanizable rubber composition comprising a reinforcing white filler, which can be used for the manufacture of a tire, wherein the rubber composition comprises a diene block copolymer which is intended to interact with said reinforcing white filler, said diene block copolymer comprising on at least one end thereof a polysiloxane block which ends in a trialkylsilyl group, said polysiloxane block corresponding to the formula:
- [—(SiR1R2O)—]x-SiR3R4R5,
- in which R1, R2, R3, R4 and R5 each represent alkyl groups having from 1 to 20 carbon atoms, and in which x is a natural integer other than zero.