Officers were called to Fenby Avenue at 11.29pm on Wednesday, January 24, after receiving a report of a window being damaged.
The arrested men, aged 22 and 20,remain in custody today while enquiries are continuing.
No injuries are reported.
Detective Inspector Andy Farrell, of the Firearms Prevent Team, said: “Our enquiries suggest that a car found burnt out in Brompton Road is linked to the discharge and we are keen to hear from anyone who saw this vehicle – a light blue Volkswagen Golf – in the area earlier that evening.
“We would also like to hear from anyone who may have seen two males acting suspiciously in the Brompton Road area at around 9pm.
“We continue to believe this was a targeted attack on a property and anyone who can assist this investigation is asked to contact the Firearms Prevent Team on 101, quoting log 1978 of 24 January.”
Information can also be reported anonymously to Crimestoppers on 0800 555111.