We study the exceptional theta correspondence for real groups obtained by restricting the minimal representation of the split exceptional group of the type
E
n
\mathbf E_n
, to a split dual pair where one member is the exceptional group of the type
G
2
\mathbf {G}_2
. We prove that the correspondence gives a bijection between spherical representations if
n
=
6
,
7
n=6,7
, and a slightly weaker statement if
n
=
8
n=8
.