Kent are seeking independent arbitration with the England and Wales Cricket Board and Hampshire over the decision to keep them in Division Two of the County Championship.
After Durham were relegated from the top flight over financial issues, Hampshire were reinstated.
Kent finished second in Division Two and believe they should have been promoted following Durham's demotion.
Kent have written to the ECB challenging their "perverse" decision.
Durham were relegated earlier this month after accepting a £3.8m financial aid package from the ECB to help them manage current and historic debts.
With Division One being restructured ahead of the 2017 campaign, two sides were relegated this season with just one side - Essex, the Division Two champions - being promoted.
Hampshire finished in the second relegation spot but were reprieved by the ECB following Durham's financial difficulties.
Kent say the governing body's stance is "wrong, procedurally flawed and in breach of fundamental legal principles".
George Kennedy, chairman of the Canterbury-based club, said the issue had left him considering his position.