City's owners struck a deal to play at Northampton's Sixfields home for the next three seasons after a long-running dispute with Arena Coventry Limited over the terms of their Ricoh rental agreement.
ACL this week said they would sign a Company Voluntary Arrangement enabling Coventry to exit administration if the League One agreed to a new 10-year lease on reduced rent.
In the meantime, ACL have complained to the Football League about City's proposed groundhsare.
A spokesman said: "It is clear that the Football League has breached its own regulations in making the deeply unpopular decision to allow a ground-sharing arrangement with Northampton.
"There is no justification to take the Sky Blues out of Coventry, and the Football League clearly have not considered the matter fully - or else they would not have arrived at this decision.
"ACL remains committed to keeping the Sky Blues in Coventry and will pursue all avenues available to us to do so."