The 48-year-old is reported to have verbally abused a black teenage boy and two white teenage girls near the taxi rank on Southbrook Road.
Following the alleged incident at around 4pm last Friday, the teenagers are said to have entered Costa coffee and the nearby Co-Op store before leaving.
Officers were called by a member of the public who claimed to have witnessed the abuse.
READ MORE: Racist abuse against Kyle Walker-Peters investigated by police
A 48-year-old man was arrested on suspicion of racially aggravated threatening, abusive and insulting words and behaviour causing harassment, alarm or distress.
He has been bailed while enquiries continue.
Officers are asking the public for help to identify the alleged victims.
A police spokesperson said: “Since the incident was reported to us, officers have followed up lines of enquiry but now we are turning to the public for your help.
“Are you the victims of this incident? Do you know who is?
“Did you witness what happened or have mobile phone footage showing the incident?
“Please get in touch by calling us on 101 or reporting online via our website ( quoting 44230097427.”