Those thoughts turned into speculation and rumor later Tuesday when ESPN's Chris Low tabbed Barnhart as a possible successor, and that report got legs as the week wore on and Tennessee moved forward into the next era.
Barnhart tripped up any speculation Thursday by telling the Lexington Herald-Leader that he plans to remain at Kentucky.
"I don't have any interest (in the UT job)," Barnhart told the Herald-Leader's Mark Story. "I've got good coaches (at Kentucky), I have a family that has settled in here, I have a son who is about to be a senior in high school."
Barnhart signed a contract extension for "exemplary performance" in February, but that extension came under President Lee T. Todd, Jr., who will retire at the end of the month. Some have wondered how Barnhart will fit with the incoming president, Dr. Eli Capilouto.
Thursday's comments seem to indicate that Barnhart looks forward to working with the new president and continuing his work at UK.
"I said when I agreed to my last contract that (Kentucky) is where I plan to be until I decide on my next path, something that will probably be outside athletics," Barnhart said in the Herald-Leader story. "I've got things I still want to accomplish here and I'm excited about doing that."