News of the World reports suggest that Cole had shot an air rifle at sport sciences student Tom Cowan having been unaware that the .22 gun was loaded.
Cowan is said to have been injured after the incident but didn't need hospital treatment after the club's medical staff came to his aid.
Now, Surrey Police have revealed that they are to probe the story and contact Chelsea in order to discover what happened during the incident.
A spokesman for the force said: “While no direct allegation has been made to Surrey Police the matter has been brought to our attention through reports in the media.
“We will be contacting the club to establish if any criminal offences has been committed.”Chelsea have also issued a statement regarding the allegations, revealing that they are likely to punish the former Arsenal man.
The statement reads: “We have fully investigated and we are taking appropriate action.
"We will not be commenting further as it is an internal matter."