It's one example, Godsey said, of how local governments can look for ways to work together for better, more efficient government.
Godsey said he is scheduled to meet with State Department of Corrections officials in Nashville next week and will broach the topic with them.
"I hope to start a dialogue about a regional jail," Godsey said. "Everyone but Hancock County is interested."
Godsey said the potential for a regional jail was discussed Monday at a First Tennessee Development District (FTDD) meeting.
The FTDD includes Carter, Greene, Hancock, Hawkins, Johnson, Sullivan, Unicoi and Washington counties.
Another topic at that meeting which highlights a need for regional cooperation was a decrease in the amount of money available for state road projects, Godsey said.
The amount of funding the Tennessee Department of Transportation (TDOT) has available for road projects statewide is "shrinking tremendously," Godsey said.
Sullivan County and each of its cities need to make a joint list of priorities to submit to TDOT instead of each entity going to Nashville with a separate wish list of road projects, Godsey said.
Godsey made the comments during a meeting with officials from Kingsport, Bristol, the county's school system, and each city's school system.
He called for the meeting earlier this month, citing a need to discuss long-term school needs and provide a forum for the wider subject of consolidation.
Comments at Tuesday's meeting focused mostly on the need for the county and cities' school systems to find ways to work together - without consolidating the systems.
The Sullivan County Commission voted more than a year ago to hire an outside consultant to conduct a study of the county system's long-term needs. Funding of $12,000 was approved, and the effort lost steam.
The issue was revived last month after County Commissioner Ralph Harr proposed a $50 million bond issue to build two new elementary schools for the county system. The full commission eventually agreed to the concept of a future bond issue for school construction projects but has asked Godsey to move ahead with procurement of the study.
Godsey said he is scheduled to meet Friday with a Knoxville firm that recently conducted a school-needs study for the city of Bristol, Tenn. That study, for a much smaller system than that of the county, cost $130,000.
County school officials need to know more about when and where each of the cities plans to grow through annexation, Godsey said, because not knowing makes planning a "nightmare."
Sullivan County School Superintendent Glenn Arwood echoed that concern.
"We need to make intelligent decisions based on what other people are going to do," Arwood said. "We need to make sure we don't locate a building that's going to be half filled."
Arwood said the county school system is currently looking at all of its facilities to prioritize needed renovations and repairs.
Arwood said there is always anxiety among residents when the potential for change arises.
"There are three outstanding school systems in Sullivan County," Arwood said. "I want all three of those systems to be viable and be as good as they can be."
Godsey said he wants to see if an agreement can be put in place to freeze the boundaries of all school districts - no matter which system they belong to - so that annexation by the cities would have no effect on where children go to school.