Those including supporters group the Sky Blue Trust, local MPs Jim Cunningham and Bob Ainsworth, Nikki Sinclaire MEP and the board of Ricoh Arena management company ACL have all signed an open letter to the League.
They have done so quoting regulation 79 of the Football League rules, which allows the League to refer any matter to a commission appointed by the FA.
It comes after the League's reluctant approval that Coventry can play their home games at Northampton's Sixfields Stadium for an initial period of three seasons while their new ground is being built, although it could stretch to as many as five.
Part of the open letter stated: "While there are threats that Coventry City FC will move to play their home games in Northampton, we still believe that a resolution to this matter is possible - and one that keeps the Sky Blues playing where they belong, in Coventry.
"The Football League has not been able to resolve this issue, and it has indicated that it might reluctantly have to allow the Sky Blues to play in Northampton if Otium Entertainment Group Limited is successful in acquiring the Football League Share for Coventry City FC.
"Otium has not, as yet, acquired the Golden Share, and there are other options available to the Sky Blues to enable them to continue playing in Coventry for the forthcoming season.
"If the Football League believes it has been put in a difficult position, then there is a procedure that the League can follow to allow the Football Association to determine the best outcome for Coventry City Football Club - and above all for its supporters."
Commenting on the letter, ACL director Peter Knatchbull-Hugessen said: "With the new season drawing ever closer, we are continuing to fight to keep the Sky Blues in Coventry. It's what we want, it's what the Football League wants, and most importantly of all, it's what Sky Blues fans want.
"The Football League's attempts to act as an honest broker have been rejected by Sisu, so we are calling on them to use their power to refer this matter to the Football Association. We hope that both bodies will take this opportunity to act in the best interests not just of Sky Blues fans but also for the good of football in this country."