Discussions had been ongoing for months between Sisu, the League One club's owners, and Arena Coventry Limited (ACL), who manage the stadium on behalf of joint owners the Alan Edward Higgs Charity and Coventry City Council.
A statutory demand for £1.1million in unpaid rent stretching back 10 months was issued to the Sky Blues in early December - a figure which now stands at £1.347m - and ACL chairman Nicholas Carter has warned "now is the time for Sisu to pay up or sell up and get out of Coventry".
ACL claim three club directors have backtracked on a verbal agreement made between the two parties towards the end of January to primarily cut the £1.28m annual rent to £400,000, as well as waive more than £300,000 of the debt amid other details including a revised share of matchday revenue.
Thursday's statement, suggesting City in response proposed alternative terms in a U-turn on that verbal agreement, also alleges an email sent by Coventry chief executive Tim Fisher stated the club had "no option but to build a new venue".
All of this comes on the same day as manager Mark Robins departed the club and agreed to take over at Championship side Huddersfield.
Amid a lengthy official statement, ACL chairman Carter said: "To spend many hours engaging in positive and constructive discussions, leading to a detailed point by point discussion of a proposed Heads of Terms Agreement resulting in verbal agreement and handshakes all round; only to then renege when it came to signing the agreement, is truly reprehensible behaviour.
"There's simply no point in continuing these discussions while the club, under Sisu's ownership, continues to behave in this manner. We will only be prepared to resume these conversations if John Clarke, Tim Fisher and Mark Labovitch sign up to the deal to which they agreed.
"If the club directors can't or won't follow through on the agreement they participated in creating, then we suggest to them that the time has come to consider offering ownership of CCFC to an outside buyer better placed to run the club's financial operations. Make no mistake, now is the time for Sisu to pay up or sell up and get out of Coventry."
Coventry vice-chairman Clarke was unavailable for comment, while there has been no official statement yet made by the club in response to ACL.