There is a significant discrepancy between the current theoretical prediction of the cosmological lithium abundance, mostly produced as 7Be during the Big Bang, and its observationally inferred value. We investigate whether the resonant enhancement of 7 Be burning reactions may alleviate this discrepancy. We identify one narrow nuclear level in 9B, E5/2+ ≃ 16.7 MeV that is not sufficiently studied experimentally, and being just ~ 200 keV above the 7Be+d threshold, may lead to the resonant enhancement of 7Be(d, γ)9B and 7Be(d, p)αα reactions. We determine the relationship between the domain of resonant energies Er and the deuterium separation width Γd that results in the significant depletion of the cosmological lithium abundance and find that (Er, Γd)≃(170-220, 10-40) keV can eliminate the current discrepancy. Such a large width at this resonant energy can be only achieved if the interaction radius for the deuterium entrance channel is very large, a27 ≥ 10 fm. New nuclear experimental and theoretical work is needed to clarify the role this resonance plays on the BBN prediction of the lithium abundance. Alternatively, the most liberal interpretation of the allowed parameters of 16.7 MeV resonance can significantly increase the errors in predicted lithium abundance: [7Li/H]BBN = (2.5-6) × 10-10.