The first-team player was quizzed by officers over possession of an illegal substance at the Rock Ness music festival, which took place on the banks of the loch last weekend.
Northern Constabulary declined to comment on the matter but it is understood the player was spoken to after a substance was recovered.
The player was not arrested and has not been charged but it is understood the force will analyse the substance.
But it could take months before the police probe determines whether the player will be charged and Caley Thistle are making their own enquiries in the meantime.
A club spokesman said: "We have been made aware of an alleged incident involving one of our players relating to a recreational drug at a music event.
"We are making our own enquiries and considering our response.
"We will need to discuss the matter with the player before finalising our position.
"We will make no further comment until after we have completed our assessment."