In June, a three-day independent judicial review, called for by the club's owners Sisu, ruled the loan was a lawful use of public funds.
The money was used by Ricoh's operators, Arena Coventry Limited (ACL), to pay off debts.
Sisu lodged an appeal at the Court of the Appeal on Friday.
The court could dismiss the case or agree to hear it or, decide to send the case to the European Courts of Justice, legal representatives said.
The appeal follows a long-running rent dispute between Sisu and the Ricoh Arena, which has seen the club play its home games at Northampton Town's ground, more than 30 miles (48km) away from Coventry, since last August.
On Thursday, the League One club paid the stadium owners £471,192 in unpaid rent.
Earlier this month, the Football League ordered Coventry to pay the stadium's operator, ACL, by 14 August.
The owners of Coventry City have lodged an appeal against a decision that endorsed the city council loaning £14m to the firm that runs the Ricoh Arena.