Collagen is a structural protein that self-assembles into fibrillar structures in the extracellular matrix. Collagen self-assembly into fibrils relies on specific interactions between these proteins. Here, we describe our studies using optical-tweezers-based passive microrheology to investigate how the removal of telopeptides - short non-helical regions flanking the triple helical domain of collagen - influences interactions between collagen molecules. We find that telopeptides contribute substantial elasticity to collagen solutions at timescales from ~10 msec to ~1 sec and telopeptide-intact collagen solutions deviate from the single-mode relaxation Maxwellian behavior at low frequencies with increasing concentration, suggesting the presence of transient telopeptide-collagen interactions.