OUP accepted manuscript

The microquasar Cygnus X-1 displays the two typical soft and hard X-ray states of a black hole transient. During the latter, Cygnus X-1 shows a one-sided relativistic radio-jet. Recent detection of the system in the high energy (HE; E greater than or similar to 60 MeV) gamma-ray range with FermiLAT associates this emission with the outflow. Former MAGIC observations revealed a hint of flaring activity in the very high-energy (VHE; E greater than or similar to 100 GeV) regime during this X-ray state. We analyse ~ to 97 h of Cygnus X-1 data taken with the MAGIC telescopes between July 2007 and October 2014. To shed light on the correlation between hard X-ray and VHE gamma rays as previously suggested, we study each main X-ray state separately. We perform an orbital phase-folded analysis to look for variability in the VHE band. Additionally, to place this variability behaviour in a multiwavelength context, we compare our results with Fermi-LAT, AGILE, Swift-BAT, MAXI, RXTE-ASM, AMI and RATAN-600 data. We do not detect Cygnus X-1 in the VHE regime. We establish upper limits for each X-ray state, assuming a power-law distribution with photon index Γ = 3.2. For steady emission in the hard and soft X-ray states, we set integral upper limits at 95 %per cent confidence level for energies above 200 GeV at 2.6 x 10⁻¹² photons cm⁻² s⁻¹ and 1.0 x 10⁻¹¹ photons cm⁻² s ⁻¹, respectively. We rule out steady VHE gamma-ray emission above this energy range, at the level of theMAGIC sensitivity, originating in the interaction between the relativistic jet and the surrounding medium, while the emission above this flux level produced inside the binary still remains a valid possibility.