Evidence for the decays B-0 -> (D) over bar (0)phi and B-0 -> (D) over bar (0) phi is reported with a significance of 3.6 sigma and 4.3 sigma, respectively. The analysis employs pp collision data at centre-of-mass energies root s = 7, 8 and 13TeV collected by the LHCb detector and corresponding to an integrated luminosity of 9 fb(-1). The branching fractions are measured to be|B(B-0 -> (D) over bar (0)phi) = (7.7 +/- 2.1 +/- 0.7 +/- 0.7) x 10(-7),|B(B-0 -> (D) over bar (0)phi) = (2.2 +/- 05 +/- 0.2 +/- 0.2) x 10(-6).|In these results, the first uncertainty is statistical, the second systematic, and the third is related to the branching fraction of the B-0 -> (D) over bar K-0(+) K- decay, used for normalisation. By combining the branching fractions of the decays B-0 -> (D) over bar (()0)phi and B-0 -> (D) over bar (()0)omega, the omega-phi mixing angle delta is constrained to be tan(2)delta = (3.6 +/- 0.7 +/- 0.4) x 10(-3), where the first uncertainty is statistical and the second systematic. An updated measurement of the branching fractions of the B-s(0) -> (D) over bar ((*)0).phi decays, which can be used to determine the CKM angle gamma, leads to|B(B-s(0) -> (D) over bar (0)phi) = (2.30 +/- 0.10 +/- 0.11 +/- 0.20) x 10(-5),|B(B-s(0) -> (D) over bar (*0)phi) = (3.17 +/- 0.16 +/- 0.17 +/- 0.27) x 10(-5).