Binding of DNA/RNA nucleobases, aromatic amino acids and heterocyclic molecules on two-dimensional silicene and germanene sheets have been investigated for the application of sensing of biomolecules using first principle density functional theory calculations. Binding energy range for nucleobases, amino acids and heterocyclic molecules with both the sheets have been found to be (0.43-1.16eV), (0.70-1.58eV) and (0.22-0.96eV) respectively, which along with the binding distances show that these molecules bind to both sheets by physisorption and chemisorption process. The exchange of electric charges between the monolayers and the incident molecules has been examined by means of Bader charge analysis. It has been observed that the introduction of DNA/RNA nucleobases, aromatic amino acids and heterocyclic molecules alters the electronic properties of both silicene and germanene nano sheets as studied by plotting the total (TDOS) and partial (PDOS) density of states. The DOS plots reveal the variation in the band gaps of both silicene and germanene caused by the introduction of studied molecules. Based on the obtained results we suggest that both silicene and germanene monolayers in their pristine form could be useful for sensing of biomolecules.