One of the defining properties of debris discs compared to protoplanetary discs used to be their lack of gas, yet small amounts of gas have been found around an increasing number of debris discs in recent years. These debris discs found to have gas tend to be both young and bright. In this paper, we conduct a deep search for CO gas in the system HD 95086 - a 17 Myr old, known planet host that also has a debris disc with a high fractional luminosity of 1.5 x 10(-3). Using the Atacama Large Millimeter/submillimeter Array (ALMA), we search for CO emission lines in bands 3, 6, and 7. By implementing a spectro-spatial filtering technique, we find tentative evidence for COJ = 2-1 emission in the disc located at a velocity, 8.5 +/- 0.2 km s(-1), consistent with the radial velocity of the star. The tentative detection suggests that the gas on the east side of the disc is moving towards us. In the same region where continuum emission is detected, we find an integrated line flux of 9.5 +/- 3.6 mJy km s(-1), corresponding to a CO mass of (1.4-13) x 10(-6) M-circle plus. Our analysis confirms that the level of gas present in the disc is inconsistent with the presence of primordial gas in the system and is consistent with second generation production through the collisional cascade.