In the context of minimal supersymmetric standard model (MSSM), we discuss the possibility of the lightest Higgs boson with mass $M_h = 98 $ GeV to be consistent with the $2.3sigma$ excess observed at the LEP in the decay mode $e^+e^- to Zh$, with $h to b {bar b}$. In the same region of the MSSM parameter space, the heavier Higgs boson $(H)$ with mass $M_H sim 125 $ GeV is required to be consistent with the latest data on Higgs coupling measurements at the end of 7 + 8 TeV LHC run with $25{rm fb}^{-1}$ of data. While scanning the MSSM parameter space, we impose constraints coming from flavour physics, relic density of the cold dark matter as well as direct dark matter searches. We study the possibility of observing this light Higgs boson in vector boson fusion process and associated production with $W/Z$ boson at the high luminosity $(3000~{rm fb}^{-1})$ run of the 14 TeV LHC. Our analysis shows that this scenario can hardly be ruled out even at the high luminosity run of the LHC. However, the precise measurement of the Higgs signal strength ratios can play a major role to distinguish this scenario from the canonical MSSM one.
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