The warning came from Origin's drilling fluid supplier Australian Mud Company, which informed the explorer that stocks of its imported product, Nutplug, has been found to contain traces of asbestos.
Titan is holding information forums for its staff on the matter and has engaged the help of a medical expert to answer questions.
Preliminary advice given to the company suggests that exposure levels will most likely be low or nil.
Titan does not expect Origin's suspension to last long, and has stated that under the terms of its contractual arrangements, the cost to the company is anticipated to be minimal.