The board members said they were unhappy to hear that tighter procedures were not in place to ensure that any undelivered alcohol would not end up in the wrong hands.
They heard that Deliveroo drivers can either keep the undelivered alcohol or “put it in a private bin”.
The issue came to light when councillors heard an application from the Co-op to allow its Laurieston store, in Mary Street, to deliver alcohol along with groceries.
And although they had previously approved two identical applications, this time they noticed the arrangements for Deliveroo staff.
Councillors were told that the vast majority of deliveries for the Laurieston store will be made by Co-op drivers and they receive the same two hours of training that their in-store colleagues do, even though this isn’t compulsory.
Speaking on behalf of the Co-op, solicitor Eilidh McGuire said that Deliveroo was primarily used in city areas and was unlikely to be used at all in Laurieston.
She said that the retailers had also had concerns at the policy but having looked into it carefully were assured there was no risk and “were comfortable with Deliveroo delivering alcohol on that basis”.
She stressed that Deliveroo was a third party service and retailers such as the Co-op were required to sign up to their conditions in order to use them.
“The Co-op would never sign up to something that would put its licence at risk,” she told board members.
Ms McGuire assured members that neither staff drivers or third party drivers will ever leave alcohol in a safe place and will always challenge anyone who looks under 25.
Councillor James Kerr said he was not comfortable that there seemed to be such a gap in procedures.
Councillor John McLuckie also expressed his concern, but added: “On the other hand, if the driver can keep it, he’s certainly not going to hand it away to someone who is under age.”
Despite their misgivings, councillors granted the licence.
Deliveroo was approached for comment.