Police Scotland is in talks with a number of Scottish universities about the proposal, which it says would make policing “more inclusive and accessible”.
But while the qualification will not replace the traditional route of entry, it is still likely to be controversial.
Assistant Chief Constable Malcolm Graham said:“We are currently exploring options for entry into the organisation that offer flexibility to enable a career in policing for a wide variety of people. The aim is to make a career in policing more inclusive and accessible to members of our communities who wish to pursue the role of police officer.
“One route of entry being examined is a further education option in collaboration with academic institutions in Scotland which wish to develop more bespoke programmes in policing.”
Under the current selection process, recruits must pass the Standard Entrance Test (SET), which is made up of questions on language, numbers and information handling. There is also a fitness assessment centring on the “bleep test”.
Earlier this week, former justice secretary Kenny MacAskill criticised plans by England’s College of Policing to have all officers educated to degree level.
Writing in Police Professional journal, Mr MacAskill said the move risked reducing the pool of recruits and making the service less representative of the communities it is there to serve.
Calum Steele, general secretary of the Scottish Police Federation, said: “Just because someone has a degree, it doesn’t make them a good police officer.
“Many good police officers have come from non-academic backgrounds and there’s no reason to believe that introducing degrees would improve the calibre of police officers. If they do introduce academic qualifications, they would only be a form of pre-qualification.”