Recent data on the differential angular distribution for the transfer reaction 11Li(p,d)10Li at E/A=5.7 MeV in inverse kinematics are analyzed within the DWBA reaction framework, using the overlap functions calculated within a three-body model of 11Li. The weight of the different 10Li configurations in the system's ground state is obtained from the structure calculations unambiguously. The effect of the 9Li spin in the calculated observables is also investigated. We find that, although all the considered models succeed in reproducing the shape of the data, the magnitude is very sensitive to the content of p1/2 wave in the 11Li ground-state wave function. Among the considered models, the best agreement with the data is obtained when the 11Li ground state contains a ∼31% of p1/2 wave in the n–9Li subsystem. Although this model takes into account explicitly the splitting of the 1+ and 2+ resonances due to the coupling of the p1/2 wave to the 3/2− spin of the core, a similar degree of agreement can be achieved with a model in which the 9Li spin is ignored, provided that it contains a similar p-wave content.