The problem of source localization from time-difference-of-arrival (TDOA) measurements is in general a non-convex and complex problem due to its hyperbolic nature. This problem becomes even more complicated for the case of multi-source localization where TDOAs should be assigned to their respective sources. We simplify this problem to an ℓ1-norm minimization by introducing a novel TDOA fingerprinting model for a multi-source scenario. Moreover, we propose an innovative trick to enhance the performance of our proposed fingerprinting model in terms of the number of identifiable sources. An interesting by-product of this enhanced model is that under some conditions we can convert the given underdetermined problem to an overdetermined one and efficiently solve it using classical least squares (LS) approaches. Our simulation results illustrate a good performance for the introduced TDOA fingerprinting.