Durham Regional Police will update reporters about the case starting at 10 a.m. ET Thursday.
Sgt. Nancy van Rooy told reporters on Wednesday afternoon that police are still working on a number of leads, but investigators do not know what happened to the 52-year-old.
"To date, he has not yet been located and to date we don’t have any conclusive evidence as to his whereabouts," she said.
Van Rooy said police are "very confident" extensive ground and air searches have covered the majority of the areas where Boucher was known to go running.
Police said social media were abuzz with rumours about the missing father of two and teacher at Bowmanville High School.
Police were asked about money found in Boucher's desk at work. Later, the school board said the money was for a class ski trip.
Van Rooy said there is no reason to believe Boucher is involved with anything criminal. She said it is possible he "stepped away" voluntarily. If that is the case, she urged him to get in touch with police to let them know he is safe.
"We have nothing that is substantive that shows there was a trigger to a change of behaviour, but if that is the explanation, let's hope so, and if Mr. Boucher or anybody else who knows his whereabouts can let us know that he is safe and sound, that's ultimately what we're looking to do," she said.
'We don't know what could have happened'
Van Rooy added there is no "electronic footprint" for the missing man — no hospital attendance or financial activity on his account since he has gone missing.
Boucher is an avid runner who has gone on early-morning jogs before work almost every day for 20 years.
It's believed Boucher set out for his usual run early on Monday from his home east of Toronto, although police have said no one actually saw him leave.
His daughter, Bettina Boucher, told CBC News that her family is trying to stay positive, but they are in the dark regarding his whereabouts.
"We’re just really confused and we don’t know what could have happened," she said Wednesday during an interview at the front door of the family’s home.