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In this paper we present the deep, wide-field and multi-band imaging of the LEO I pair NGC~3379-NGC~3384, from the VST Early-type GAlaxy Survey (VEGAS). The main goal of this study is to map the intra-group baryons in the pair, in the form of diffuse light and globular clusters (GCs). Taking advantage from the large covered area, which extends for $\sim$ 3.9 square degrees around the pair, and the long integration time, we can map the light distribution out to $\sim$ 63 kpc and down to $\sim$ 30 mag/arcsec$^2$ in the $g$ band and $\sim$ 29 mag/arcsec$^2$ in the $r$ band, deeper than previous data available for this target. The map of the intra-group light (IGL) presents two very faint ($μ_g \sim$ 28-29 mag/arcsec$^2$) streams protruding from the brightest group member NGC~3379 and elongated toward North-West and South. We estimate that the fraction of the stellar halo around NGC~3379 plus the IGL is $\sim 17 \pm 2\%$ in both $g$ and $r$ bands, with an average color $g$-$r$= $0.75 \pm 0.04$~mag. The color distribution of the GCs appears multi-modal, with two dominant peaks at (u-r) = 1.8 mag and (u-r) = 2.1 mag, respectively. The GC population stretches from North-East to South-West and from North-West to South of the pair, in the last case overlapping with the streams of IGL, as well as the PNe distribution found by \citet{Hartke2020} and \citet{Hartke2022arXiv220108710H}. Since these structures are elongated in the direction of the two nearby galaxies M96 and NGC~3338, they could be the remnant of a past gravitational interactions with the pair.