Aims. The origin of the observed variability of the gas-phase D/H ratio in the local interstellar medium is still debated, and in particular the role of deuterium depletion onto dust grains. Here we extend the study of the relationship between deuterium and titanium, a refractory species and tracer of elemental depletion, and explore other relationships. Methods. We have acquired high resolution spectra for nine early-type stars using the VLT/UVES spectrograph, and detected the absorption lines of interstellar TiII. Using a weighted orthogonal distance regression (ODR) code and a special method to treat non symmetric errors, we compare the TiII columns with the corresponding HI, DI and also OI columns. In parallel we perform the same comparisons for available FeII data. Results. We find a significant correlation between TiII/HI and D/H in our data set, and, when combined with published results, we confirm and better constrain the previously established trends and extend the trends to low HI columns. We exclude uncertainties in HI and OI columns as the main contributor to the derived metals-deuterium correlations by showing that the TiII/HI ratio is positively correlated with DI/OI. We find a similar correlation between FeII/HI and DI/OI. The TiII gradients are similar or slightly smaller than for FeII, while one would expect larger variations on the basis of the higher condensation temperature of titanium. However we argue that ionisation effects introduce biases that affect iron and not titanium and may explain the gradient similarity. We find a less significant negative correlation between the TiII/DI ratio and the hydrogen column, possibly a sign of different evaporation of D and metals according to the cloud properties. More TiII absorption data along very low H column lines-of-sight would be useful to improve the correlation statistics.