The incident happened between 2pm and 3pm on Friday, January 15, when the 54-year-old victim was on a pathway in the wooded area of the park in Kettering Road.
He passed a small, white, long-haired terrier which, without provocation, bit him on the right ankle.
The man suffered puncture wounds which required antibiotics.
The dog was being walked by a man about 60 years old and 5ft 8in with grey hair.
He was with a woman of a similar age who had shoulder-length grey hair.
She was about 5ft 2in and was walking a medium-sized, long-haired brown dog.
Police would like to identify these people and would also like to hear from anybody who witnessed the incident.
Witnesses or anyone with information about this incident is asked to contact police on 101 or Crimestoppers anonymously on 0800 111 555.