The Independent Police Complaints Commission (IPCC) confirmed the individuals were a mixture of retired and serving officers.
It said 11 had already been interviewed under caution. A spokesman said the other two would be interviewed in the near future.
Fresh inquests into the 96 deaths will begin in Warrington on Monday.
The IPCC spokesman said four of the 13 had been identified as suspects as part of its investigation and also Operation Resolve, the criminal investigation into the tragedy.
The IPCC’s inquiry covers the actions of the police in the aftermath of the crush at Hillsborough.
The football supporters were crushed during the FA Cup semi-final between Liverpool and Nottingham Forest at Sheffield Wednesday’s stadium on 15 April 1989.