  We present a proposal to relate the de Sitter Conjecture (dSC) to the
Covariant Entropy Bound (CEB). By assuming an early phase of accelerated
expansion where the CEB is satisfied, we take into account a contribution from
extra-dimensions to the four-dimensional entropy which restricts the values of
the usual slow-roll parameters. We show in this context that the dSC
inequalities follow from the CEB -- including their mutual exclusion -- in both
single and multi-field inflationary scenarios. We also observe that the order
one constants, c and c' in the conjecture are given in terms of physical
quantities such as the change in entropy over time, the Hubble constant and the
dynamics of the effective scalar fields. Finally, we give a simple example to
illustrate a possible contribution to the four-dimensional entropy from a flux
string scenario.
