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Mr O'Connor says he cannot recall driving in an erratic or alarming way, was not involved in any accidents or near-misses, and would be happy to talk to police.
Police said a member of the public contacted them about a car being driven on State Highway 6, the Gibbston Highway, east of Queenstown, about 8.45pm on Wednesday.
Police searched for the vehicle, registered to Mr O'Connor, but could not find it on Wednesday night. They said yesterday they would be following up on the report.
O'Connor confirmed that he was on SH6 on Wednesday night as he drove his son Michael from Christchurch to Queenstown while on holiday. He had no idea what the member of the public's concern might be about.
"I can't think of anything it might relate to.
"I was travelling with my autistic son and if he ever needs attention, I try to pull over," Mr O'Connor said.
"I'd be interested to know what the perception was. I'd be very, very surprised if someone thought I was speeding.
"I can't recall anything, certainly nothing that resulted in a near-miss or anything like that. I'm scratching my head."
Asked whether he had been drinking, he said: "I don't drink."
He said police had not been in touch with him, but was happy to talk to them.
"I'll just wait to hear from police."
A police spokesman said the member of the public had contacted police because of "the manner in which the vehicle was being driven".
"The vehicle was not located at the time. This report will be followed up by police."
O'Connor was the longest-serving president of the Police Association before he became the MP for Ohariu in 2017.
Before that, he was a police officer, rising to the rank of senior sergeant, and once spent 18 months undercover in the drug and gang scene in the North Island.
In 1995 he became the association's president, a position he held until 2016.
He also spent eight years as the chairman of the International Council of Police Representative Associations, representing 1.5million officers from more than 30 countries.
He was awarded life membership of the Police Association in 2017.