  The detection of gravity modes is expected to give us unprecedented insights
into the inner dynamics of the Sun. Within this framework, predicting their
amplitudes is essential to guide future observational strategies and seismic
studies. In this work, we predict the amplitude of low-frequency asymptotic
gravity modes generated by penetrative convection at the top of the radiative
zone. The result is found to depend critically on the time evolution of the
plumes inside the generation region. Using a solar model, we compute the GOLF
apparent surface radial velocity of low-degree gravity modes in the frequency
range $10~\mu H_z\le \nu \le 100~\mu H_z$. In case of a Gaussian plume time
evolution, gravity modes turn out to be undetectable because of too small
surface amplitudes. This holds true despite a wide range of values considered
for the parameters of the model. In the other limiting case of an exponential
time evolution, plumes are expected to drive gravity modes in a much more
efficient way because of a much higher temporal coupling between the plumes and
the modes than in the Gaussian case. Using reasonable values for the plume
parameters based on semi-analytical models, the apparent surface velocities in
this case turn out to be one order of magnitude smaller than the 22-years GOLF
detection threshold and than the previous estimates considering turbulent
pressure as the driving mechanism, with a maximum value of $0.05$ cm s${}^{-1}$
for $\ell =1$ and $\nu\approx 100~\mu H_z$. When accounting for uncertainties
on the plume parameters, the apparent surface velocities in the most favorable
plausible case become comparable to those predicted with turbulent pressure,
and the GOLF observation time required for a detection at $ \nu \approx100~\mu
H_z$ and $\ell=1$ is reduced to about 50 yrs.
