The SOLIS (Seeds Of Life In Space) IRAM/NOEMA Large Program aims at studying a set of crucial complex organic molecules in a sample of sources, with well-known physical structure, covering the various phases of Solar-type star formation. One representative object of the transition from the prestellar core to the protostar phases has been observed toward the Very Low Luminosity Object (VeLLO) called L1521F. This type of source is important to study to make the link between prestellar cores and Class 0 sources and also to constrain the chemical evolution during the process of star formation. Two frequency windows (81.6-82.6 GHz and 96.65-97.65 GHz) were used to observe the emission from several complex organics toward the L1521F VeLLO. Only 2 transitions of methanol (A+, E2) have been detected in the narrow window centered at 96.7 GHz (with an upper limit on E1) in a very compact emission blob (~7 corresponding to ~1000au) toward the NE of the L1521F protostar. The CS 2-1 transition is also detected within the WideX bandwidth. Consistently, with what has been found in prestellar cores, the methanol emission appears ~1000au away from the dust peak. The location of the methanol blob coincides with one of the filaments previously reported in the literature. The Tex of the gas inferred from methanol is (10$pm$2) K, while the H2 gas density (estimated from the detected CS 2-1 emission and previous CS 5-4 ALMA obs.) is a factor >25 higher than the density in the surrounding environment (n(H2) >10$^{7}$ cm$^{-3}$). From its compactness, low excitation temperature and high gas density, we suggest that the methanol emission detected with NOEMA is either a cold and dense shock-induced blob, recently formed ($leq$ few hundred years) by infalling gas or a cold and dense fragment that may have just been formed as a result of the intense gas dynamics found within the L1521F VeLLO system.