Fire Chief Scott Damon of Cambridge Township, Mich., told searchers that John Skelton, the boys' father, "may have just dumped them on the road," The Detroit News reports.
Morenci, Mich., Police Chief Larry Weeks also said Monday police have poked holes in the story put forward by Skelton, who is being treated in an Ohio hospital for "mental health issues" after a suicide attempt.
He told investigators he dropped off the boys, 9-year-old Andrew, 7-year-old Alexander and 5-year-old Tanner, on Friday morning with a woman by the name of Joann Taylor, whom he allegedly met online.
Police have now ruled out a connection between Skelton and a woman of that name.
Skelton had claimed that Taylor agreed to take the boys home to their mother, Tanya Skelton, so that they would not witness his attempt to hang himself. The boys were reported missing Friday by Tanya Skelton (the couple are separated).
Authorities now believe that Skelton, 39, may have driven his sons to an area in Ohio between 2:30 p.m. Thursday and 1:30 p.m. Friday, when they were reported missing, Weeks said.
Evidence shows Skelton's blue 2000 Dodge Caravan may have been in that area between 4 a.m. and 7 a.m. Friday, he said, adding, "We've collected information from a number of sources."
John Skelton has not been named as a suspect, but Weeks said they also haven't ruled him out.
The boys were with their father as part of court-ordered visitation, according to reports, and were last seen Thursday in the backyard of their father's southern Michigan home. Police say they "remain hopeful" the children are still alive.