We investigate the possibility of observing very small amplitude low frequency solar oscillations with the proposed laser interferometer space antenna ( LISA ) . For frequencies \nu below 3 \times 10 ^ { -4 } ~ { } { Hz } the dominant contribution is from the near zone time dependent gravitational quadrupole moments associated with the normal modes of oscillation . For frequencies \nu above 3 \times 10 ^ { -4 } ~ { } { Hz } the dominant contribution is from gravitational radiation generated by the quadrupole oscillations which is larger than the Newtonian signal by a factor of the order ( 2 \pi r \nu / c ) ^ { 4 } , where r is the distance to the Sun , and c is the velocity of light . The low order solar quadrupole pressure and gravity oscillation modes have not yet been detected above the solar background by helioseismic velocity and intensity measurements . We show that for frequencies \nu \lesssim 2 \times 10 ^ { -4 } ~ { } { Hz } , the signal due to solar oscillations will have a higher signal to noise ratio in a LISA type space interferometer than in helioseismology measurements . Our estimates of the amplitudes needed to give a detectable signal on a LISA type space laser interferometer imply surface velocity amplitudes on the sun of the order of 1 - 10 mm/sec in the frequency range 1 \times 10 ^ { -4 } -5 \times 10 ^ { -4 } ~ { } { Hz } . If such modes exist with frequencies and amplitudes in this range they could be detected with a LISA type laser interferometer .