Bryson, a first-term state senator from Franklin, would neither confirm nor deny this report.
It is not known whether Bryson will vacate his state Senate seat to mount his campaign. Legislators and the governor are barred from raising campaign funds while the legislature is in session.
Should Bryson resign, the Williamson County Commission would appoint someone to complete his term, which ends this year.
The deadline to file for governor, state House, or state Senate is next Thursday, April 6.
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