It is reported that a person poured a flammable liquid through the letterbox of a home in Queens Road at around 2.45am on Monday 23 November 2020.
The door was then set alight, however an occupant was able to extinguish it without sustaining any injuries.
Officers have carried out house to house enquiries, and reviewed CCTV from the area, and believe that the suspect ran from the scene towards Palmer Avenue.
A 40-year-old woman and a 19-year-old man, both from Gravesend, were also arrested in connection with the incident and released on bail, pending further enquiries, until 23 and 27 December respectively.
Investigators are now appealing for anyone with information, who is yet to speak with an officer, to get in contact.
In particular, they would like to hear from anyone with privately held CCTV in the area.
Anyone with information is asked to call Kent Police on 01474 366149 quoting 46/208800/20.