We investigated the effect of a Mg-Al layer insertion at the bottom interface of epitaxial Fe/$MgAl_{2}O_{4}$/Fe(001) magnetic tunnel junctions (MTJs) on their spin-dependent transport properties. The tunnel magnetoresistance (TMR) ratio and differential conductance spectra for the parallel magnetic configuration exhibited clear dependence on the inserted Mg-Al thickness. A slight Mg-Al insertion (thickness < 0.1 nm) was effective for obtaining a large TMR ratio above 200% at room temperature and observing a distinct local minimum structure in conductance spectra. In contrast, thicker Mg-Al (> 0.2 nm) induced a reduction of TMR ratios and featureless conductance spectra, indicating a degradation of the bottom-Fe/$MgAl_{2}O_{4}$ interface. Therefore, a minimal Mg-Al insertion was found to be effective to maximize the TMR ratio for a sputtered $MgAl_{2}O_{4}$-based MTJ.