  We investigate pairing states realized at the (001) interface of a
spin-triplet superconductor Sr$_2$RuO$_4$ on the basis of microscopic
calculations. Because of a Rashba-type spin-orbit interaction induced at the
interface, strong parity-mixing of Cooper pairs between a spin-singlet state
and a spin-triplet state occurs in this system. There are also strong
inter-band pair correlations between the spin-orbit split bands, in spite of
the considerably large spin-orbit splitting. This is due to frustration between
the spin-orbit interaction and pairing interactions. In this pairing state,
time-reversal symmetry is restored, in contrast to the bulk Sr$_2$RuO$_4$ which
is believed to be a chiral $p+ip$ superconductor with broken time-reversal
symmetry. It is demonstrated that, because of these features, the pairing state
at the interface is a promising candidate for the recently proposed
time-reversal invariant topological superconductor.
