In this paper, we have explored the framework of compressed sensing (CS) and sparse representation (SR) to reduce the footprint of unit selection based speech synthesis (USS) system. In the CS based framework, footprint reduction is achieved by storing either CS measurements or signs of CS measurements, instead of storing the raw speech waveforms. For efficient reconstruction using CS measurements, the speech signal should have a sparse representation over a predefined basis/dictionary. Hence, in this work, we have also studied the effectiveness of sparse representation for compressing the speech waveform. The experimental results are demonstrated using an analytical dictionary (DCT matrix), and several learned dictionaries, derived using K-singular value decomposition (KSVD), method of optimal directions (MOD), greedy adaptive dictionary (GAD) and principal component analysis (PCA) algorithms. To further increase compression in SR based framework of footprint reduction, the significant coefficients of sparse vector are selected adaptively, based on the type of speech segment (e.g., voiced, unvoiced etc.). Experimental studies on two different Indian languages suggest that CS/SR based footprint reduction methods can be used as an alternative to existing compression methods employed in USS system.