Det.-Sgt. Gary Giroux said he put in the request in the past few days.
"I've made the invitation through the mayor's chief of staff," Giroux said.
"That invitation, I'm going to pursue."
On Thursday, the city's chief of police made the jaw-dropping announcement that investigators had recovered a video earlier reported as appearing to show the mayor smoking crack cocaine and making racist and homophobic slurs.
The comments by Chief Bill Blair angered Ford's supporters, who railed against him for convicting the embattled mayor in public.
"He could barely contain the smirk on his face," Ford's lawyer, Dennis Morris, told Newstalk 1010.
Morris, who called on Blair to resign, said the chief should release the video.
"The video exists. He's seen it. Let the public see it. Let the public judge for themselves. I'd love to see it."
Legal experts, however, said Ford has no right to call for the video to be made public given that it is now evidence in the extortion case against his friend and occasional driver, Alexander (Sandro) Lisi.
Bill Trudell, an experienced criminal lawyer, said the video can only become public if it is introduced at trial.
"If it's evidence against one particular person, then other people don't have a right to say, 'Release it,'" Trudell said.
"A political agenda can't trump a presumption of innocence."
If, for example, Lisi were to make a plea deal, the video might not see the light of day unless the courts order it released in the public interest, Trudell said.
While Blair said Thursday that it would be up to the courts to make decisions about the video, he did offer some personal thoughts on what it apparently shows.
"As a citizen of Toronto I'm disappointed," Blair told the media.
"This is a traumatic issue for the citizens of this city and for the reputation of this city and that concerns me."
Blair's spokesman said the chief wasn't just speaking off the cuff.
"Chief Blair sought and took legal advice from two very experienced and distinguished lawyers prior to the news conference," spokesman Mark Pugash said Friday.
"No one should be surprised: these are extremely important matters and due diligence is something that has to be done."
Ford's brother, Coun. Doug Ford, also called Friday for the video to be released and denounced Blair for expressing personal opinions on such a sensitive topic.
But the councillor, who has been his brother's biggest booster, appeared to soften some of his supportive statements.
"Over the years, we use bad judgment sometimes," he told Toronto's AM640. "Yes, Rob's probably used bad judgment sometimes."
Ford himself said Thursday he could not comment on Blair's revelation because the matter is before the courts. He's previously said the video did not exist and that he does not smoke crack cocaine.
Police recovered the video — first reported by website Gawker and the Toronto Star in May — in connection with an investigation that led to extortion charges against Lisi, 35.
Blair said there were no grounds to charge Ford as a result of the recovered video.
Lisi, who also faces drug-trafficking charges, was granted bail Friday.