Currently significant efforts are devoted to designing small molecules able to bind selectively to guanine-quadruplexes (G4s). These non-canonical DNA structures are implicated in various important biological processes and have been identified as potential targets for drug development. Previously, we reported a series of triphenylamine(TPA)-based compounds including macrocyclic polyamines, which display high affinity towards G4 DNA. Following from this initial work, herein we present a series of second-generation compounds, in which the central TPA has been functionalised with flexible and adaptive linear polyamines, aiming to maximise the selectivity towards G4 DNA. The acid-base properties of the new derivatives have been studied by means of potentiometric titrations, UV-Vis and fluorescence emission spectroscopies. The interaction with G4s and duplex DNA has been explored using FRET melting assays, fluorescence spectroscopy and circular dichroism. Compared to our previously TPA derivatives with macrocyclic substituents, the new ligands reported herein retain the G4 affinity, but display two orders of magnitude higher selectivity for G4 vs. duplex DNA, most likely due to the ability of the linear substituents to embrace the G4 structure.