In this work, the sensitivity and reactivity of graphene like 2D nanosheets such as BNNS, AlNNS, GaNNS and InNNS towards ciclopirox (CPX), 5-fluorouracil (5-FU) and nitrosourea (NU) anticancer drugs have been investigated by DFT calculations. The adsorption energies and charge transfer calculations predict that among the four nanosheets, GaNNS is more attractive towards the CPX and 5-FU drugs whereas InNNS show more absorptivity towards NU drug in both gas as well as water media. The obtained adsorption energies for CPX/ GaNNS, 5-FU/GaNNS and NU/InNNS are -1.39, -0.84 and -0.82 eV respectively. Dipole moment and COSMO surface analysis predicted that AlNNS and GaNNS show more solubility in solvent media like water media. QTAIM analysis suggests that non-covalent interaction occurred in all complexes except 5-FU/AlNNS, CPX/ GaNNS and 5-FU/GaNNS where partially covalent and partially electrostatic interaction occurs in the complexes. Therefore, among the four nanosheets GaNNS may be used as promising nanocarrier for CPX and 5-FU whereas InNNS for NU anticancer drug.