  Low dust opacity spectral indices ($\beta < 1$) measured in the inner
envelopes of class 0/I young stellar objects (age $\sim 10^{4-5}$ yr) have been
interpreted as the presence of (sub-)millimetre dust grains in these
environments. The density conditions and the lifetimes of collapsing envelopes
have proven unfavorable for the growth of solids up to millimetre sizes. As an
alternative, magneto-hydrodynamical simulations suggest that protostellar jets
and outflows might lift grains from circumstellar discs and diffuse them in the
envelope. We reframe available data for the CALYPSO sample of Class 0/I sources
and show tentative evidence for an anti-correlation between the value of
$\beta_{1-3mm}$ measured in the inner envelope and the mass loss rate of their
jets and outflows, supporting a connection between the two. We discuss the
implications that dust transport from the disc to the inner envelope might have
for several aspects of planet formation. Finally, we urge for more accurate
measurements of both correlated quantities and extension of this work to larger
samples, necessary to further test the transport scenario.
