Police are continuing to work round the clock and are pursuing a number of lines of enquiry following the incident in the early hours of Thursday, May 23.
Police were called at 12.02am to reports of gun shots heard in Hazel Hill Crescent.
The incident did not result in any injuries although damage was caused to a property.
Officers are appealing to anyone who witnessed the incident, specifically anyone who may have seen a man wearing dark clothing getting on a motorbike around the time of the incident.
Detective Inspector Gayle Hart said: "We've increased patrols in the area to provide reassurance to the local community and we want people to know that we're treating this incident very seriously and doing everything we can to trace those responsible.
"We believe this was targeted and not a random attack and we do not believe that there is a risk to the wider community.
"We have teams of officers who are continuing to work hard on this case to establish what happened but we'd still like to hear from anyone with information that could help our investigation.
"Did you drive past the area at the time and haven't checked your dashcam footage yet? It could have vital information about who was in the area at the time, even if it didn't capture the incident itself. I'd urge you to please get in touch."
Chief Inspector for the local area Steve O'Neill added: "We have really strong links with the local community and I'd encourage the residents of Bestwood Park to work with us and with our local beat team by reporting any information they have. Even the smallest piece of information could be crucial to our investigation.
"As you may expect, there will be a greater police presence in the area while enquiries are made and patrols are conducted. I'd invite residents to speak to the officers if they have any concerns and I’d urge anyone with any information about this incident to contact us.
"If you have any information please call us on 101 quoting incident number 3 of 23 May 2019 or call Crimestoppers anonymously on 0800 555 111."