Last Friday, the Scottish outfit announced that they had accepted the resignations of the manager, assistant coach and head of recruitment.
The Gers claimed that they agreed to waive their right to compensation so that Warburton and his backroom team could make the process of joining another club much smoother.
However, the trio have rejected the claims, insisting that they did not formally offer to step down from their roles at Ibrox.
A joint statement released via the League Managers' Association read: "Much has been said over the last few days relating to our departure from Rangers Football Club. At this stage, for legal reasons, it is inappropriate for us to comment in any great detail on our departure from the club.
"However, given that the club has seen fit to make detailed public statements, it is important that we should clarify certain matters and as such we would like to formally place on record, that at no stage did we resign from our positions at Rangers.
"It is a matter of surprise to us, and to the League Managers Association (LMA), which is advising all three of us, that despite its detailed public statements, the club has not answered key questions put to it by the LMA, in writing, requesting an explanation of why it suggested that we resigned from our positions.
"For all three of us, it was an absolute privilege to be given the opportunity to work at a club that is so rich in tradition and history."
Warburton guided Rangers to the Scottish Championship crown and Scottish Challenge Cup during his one-and-a-half-year stay.