David Sweat, 34, and Richard Matt, 48, cut their way out of prison using power tools.
Police believe the men thought Vermont would be a “cooler” destination with fewer officers on their tail, Governor Peter Shumlin said.
Vermont was working to get the “dangerous men” locked up, officials said.
Addressing some of the 450 officers involved in the search New York Governor Andrew Cuomo said: “Follow every lead you have.
“Follow them as if it’s the lead that’s going to break the case. I am confident we are going to find them, the only question is when.”
The manhunt in northern New York and surrounding areas has now extended to campsites and boat slips in neighboring Vermont.
Governors Peter Shumlin and Andrew Cuomo held a joint press conference outside the maximum security prison from where the men escaped, Clinton Correctional Facility.
Referring to the unspecified information about the men’s whereabouts, Peter Shumlin said: “New York was going to be hot. Vermont would be cooler, in terms of law enforcement.”
Police confirmed on June 10 that they had interviewed “one woman in particular” who may have befriended the inmates and had a role in David Sweat and Richard Matt’s escape, but would not go into detail.
That woman “may had had some role in assisting them”, said New York State police Superintendent Joseph D’Amico.
An unnamed source told CNN earlier that woman is Joyce Mitchell, who worked at the prison tailor shop.
Joyce Mitchell had planned to pick up Richard Matt and David Sweat after they escaped but changed her mind at the last minute.
She has not been arrested or charged, and her son has said his mother would not have helped the prisoners escape.
Richard Matt was given a jail term of 25 years to life for beating a man to death in 1997.
David Sweat was serving a life sentence without parole for the murder of Broome County Sheriff’s Deputy, Kevin Tarsia.
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