OGV Energy have received communication with staff currently on the Transocean rig Paul B Lloyd, contracted by BP.
Two Greenpeace activists confirmed they climbed on to the rig on Sunday evening, calling for BP to end drilling for new oil wells.
Greenpeace said the 27,000-tonne rig owned by Transocean was on its way to the Vorlich field to drill new oil wells operated by BP.
One member of the work force on board the asset confirmed they have been kept inside since Sunday, another confirmed the activists had a shift change on Monday night and it is now two males.
Workers on board have been advised that BP’s legal teams are working on the situation and no one should interfere.
It is believed a number of roughnecks are patrolling the activists and they spent most of Monday sleeping and confirming they are not leaving anytime soon.
Police Scotland said it was working with the operators, Cromarty Firth Port Authority and others in an effort to resolve the situation as "safely as possible".
The Cromarty Firth is a sheltered area of sea, north of Inverness, used for parking oil and gas rigs and platforms when not in use, or when they are undergoing refurbishment.