Recently, the introduction of novel deep eutectic solvents having a hydrophobic character with greener starting materials has motivated researchers to explore these water-immiscible solvents, owing to their new potential applications. In this regard, herein atomistic molecular dynamics simulations have been performed to understand the bulk phase morphology present in dl-menthol based hydrophobic deep eutectic solvents (HDESs) with organic acids of different chain lengths used as hydrogen bond donors. From the appearance of a prepeak in the simulated total X-ray scattering structure function (S(q)), we found an evidence of intermediate-range structural organization in these HDESs. We show that the prepeak originates from the self-segregation of dl-menthol and the polar hydroxyl groups of the acids, as witnessed from partitioning of the total S(q). Surprisingly, even for a very long tail containing HDES, the apolar-apolar component shows only nominal contribution to the prepeak. We show that the structure of these HDESs is dominated by a set of very strong intermolecular hydrogen bonding between menthol-menthol, acid-acid, and menthol-acid molecules. Our results show that there is competition between the hydroxyl hydrogen of the acids and menthol to form an intermolecular hydrogen bond with the carbonyl oxygen of the acids and hydroxyl oxygen of menthol.