Detective Sergeant Craig Farrant said there had been three calls from members of the public with information, but the tip-offs appeared to be unrelated to the attempted abduction.
Police were waiting for a report from an interview with the boy carried out by a child specialist, before deciding where to take the investigation.
Prebbleton residents have been caught off guard by the abduction claim.
When the Selwyn Times canvassed the township yesterday, only one person was aware of the incident.
Prebbleton Preschool staff member Julia Whitley said a several local parents were "really concerned".
"We had some parents who live around the area where it happened come in and say, 'Have you heard?'
"People say, 'Oh my goodness, that's so close to home'."
Mrs Whitley said the concerned parents were happy with Prebbleton School's attitude.
"The parents said the school is really up with stranger danger," she said.
"We're always telling the children [at preschool] about safety and dangers in the street and stuff like that."
Detective Sergeant Farrant said there was no indication of what the motive might have been for the apparent abduction attempt.
"There have been no other reported incidents around that area at all. There's no other evidence at all pointing to this being an ongoing thing or there being a predator on the loose," he said.
"We do not believe there is any cause for residents to be concerned."
Call Detective Sergeant Farrant on 03 363 7400, or Crimestoppers on 0800 555 111, with any information.
