We present the R-band polarimetric results towards two nebulae L1415 and L1389 containing low luminosity stars. Aim of this study is to understand the role played by magnetic fields in formation of low luminosity objects. Linear polarization arise due to dichroism of the background starlight projected on the cloud providing the plane-of-the sky magnetic field orientation. The offsets between mean magnetic field directions obtained towards L1415 and L1389 and the projected outflow axes are found to be 35• and 12• , respectively. The offset between cloud minor axes and mean envelope magnetic field direction in L1415 and L1389 are 50• and 87• , respectively. To estimate the magnetic field strength by using the updated Chandrasekhar-Fermi relation, we obtained the 12 CO(J=1-0) line velocity dispersion value towards L1415 cloud using the TRAO single dish observations. The values of B pos in L1415 and L1389 are found to be 28 µG and 149 µG using CF technique and 23 µG and 140 µG using structure function analysis, respectively. The values of B pos in these clouds are found to be consistent using both the techniques. By combining the present results with those obtained from our previous study of magnetic fields in cores with VeLLOs, we attempt to improve the sample of cores with low luminosity protostars and bridge the gap between the understanding of importance of magnetic fields in cores with VeLLOs and low luminosity protostars. The Results of this work and that of our previous work show that the outflow directions are aligned with envelope magnetic fields of the clouds.