The reports quote police and Murphy as saying 49-year old John Krueger is the person of interest.
Krueger was arrested yesterday on an unrelated felony warrant charge.
Murphy says police interviewed Krueger in reference to the homicide -- and says police have considered everyone they've interviewed to be "persons of interest."
But he says he cannot comment on whether Krueger is still a person of interest.
Murphy says officers conducted a search warrant at Krueger's home.
He says krueger has a long criminal record, and prison records show seven convictions in Jackson County since 1987.
Police found Bost's body in a car parked in an alley last Tuesday afternoon.
They believe bost was killed early in the morning that day ... then her body was placed in her car with her dog, and driven to the one thousand block of East Sutherland.
If you have any information, call Altus' Crime Stoppers.
That number is (580) 482-TIPS.