Novel insights on the magnetic, ferroelectric and magnetoelectric coupling of the nano composites of BiFeO3 (BFO) and La0.7Sr0.3Mn0.95Fe0.05O3 (LSMFO) with the latter exhibiting colossal magnetoresistance (CMR) behavior are provided in this study for the first time. Appreciable magnetoelectric coupling is observed in the composite and is seen to be significantly varying at temperatures below the blocking temperature of LSMFO. The local structure and magnetic properties of both the BFO and LSMFO particles in the composite are investigated in a detailed manner using Mössbauer spectroscopy studies specially devised to address the problem concerned. Enhanced values of the effective magnetic fields are observed at the Fe sites associated with BFO particles which are in contact with LSMFO particles. Interestingly, an appreciable increase in the magnetic hyperfine fields at Fe sites corresponding to LSMFO is also observed in the nanocomposites. New insights are derived based on the results of Mössbauer studies toward comprehending the magnetic and magnetoelectric coupling effects as deduced in these composites.