We analyse a sample of 24 damped Lyman- \alpha ( DLA ) /moderate DLA systems at intermediate redshifts , 0.3 < z _ { abs } < 2.2 , all with measurement of the weak Mn ii absorption lines , to investigate which elemental ratios could possibly be used as tracers of either dust depletion or nucleosynthesis effects . We applied a component-by-component analysis to the five systems of the sample with new observations and , using this procedure , re-analyzed data gathered from the literature whenever possible . We show that the standard method which uses column densities integrated over the whole absorption profiles could substantially underestimate the abundance of rare elements relative to Fe . We find a correlation between the observed [ Si/Fe ] and [ Zn/Fe ] ratios , present in our sample at the 2.9 \sigma significance level . This correlation is fully consistent with a dust depletion sequence only for a Galactic warm disk cloud or halo cloud depletion pattern . The correlation between [ Mn/Fe ] and [ Zn/Fe ] , detected at the 3.2 \sigma significance level , can not be accounted for by any dust depletion sequence : it implies either variations of the intrinsic Mn abundance relative to Fe from -0.3 to +0.1 dex and/or a relation between depletion level and metallicity . The correlation between [ Mn/Fe ] and metallicity ( 2.6 \sigma significance level ) strengthens the assumption of intrinsic variations of [ Mn/Fe ] although some marginal correlation between [ Zn or Si/Fe ] and [ Zn/H ] is present as well . Extension of the sample toward low metallicity is needed to confirm the correlation between depletion level and metallicity . The variations of [ Ti/Fe ] vs. [ Zn/Fe ] can not be fitted by a single dust depletion sequence either . We then adopt a warm disk cloud or halo cloud depletion pattern and compare the resulting dust-corrected abundance ratios to those observed in Galactic and SMC stars . At high metallicity , [ Fe/H ] _ { dc } \ga - 0.5 , the intrinsic abundance pattern of Si , Ti , Cr and Mn in DLA absorbers closely follows the trends observed in Galactic stars and these absorbers should thus have a chemical evolution similar to that of our Galaxy . At lower metallicity , some absorbers do follow the trends present in Galactic stars but a substantial fraction of them have elemental ratios ( in particular [ Si/Fe ] _ { dc } and [ Mn/Fe ] _ { dc } ) closer to the solar values than Galactic stars . This could be explained by a larger contribution of type Ia supernovae to the chemical enrichment of these DLA absorbers than in Galactic stars of similar metallicity . This metal-poor DLA absorber population could trace H i -rich dwarf galaxies .