Burglars broke into The Portland Collection Gallery on the estate between 9.45pm and 10pm on Tuesday November 20.
They stole the Portland Tiara - a national treasure that has been seen by countless members of the public - and the diamond brooch from an armoured glass display case while the alarms were sounding.
Officers have now released CCTV of three men they would like to speak to in connection with the incident.
They are also appealing for information about a silver Audi RS5 Quattro, registration number KY61 USJ, believed to be involved in the burglary. The car is the same model as the one pictured.
The silver Audi was stolen from the Phoenix Park Park and Ride tram stop, Millennium Way East, Cinderhill, Nottingham, on Friday November 2. It was found abandoned and burnt out in Cross Lane, Blidworth, about half-an-hour after the burglary November 20.
Detective Inspector Gayle Hart said: "Our enquiries are ongoing and we're making a plea to potential witnesses.
"The suspects were wearing white suits and motorcycle helmets but we're still hoping someone may know who they are and we're urging anyone with any information to get in touch with us.
"We're also urging anyone who has any information about the silver Audi RS5 to contact us.
"Did you see this car in the area around the time of the burglary or have dash-cam footage of it? Did you see anyone in the car?
"We're keen to trace this vehicle's movements preceding the burglary so again we're appealing to anyone who saw it or who has any information to get in touch with us as soon as possible.
"We believe the burglars used specialist diamond cutter-type tools to break through the armoured glass display case. If anyone has information about people hiring or sourcing such equipment then we’d urge them to get in touch."
Anyone with any information is asked to call police on 101, quoting incident number 856 of November 20 2018, or Crimestoppers anonymously on 0800 555 111.