The animal charity and the union are currently in talks about plans to introduce a performance-related pay scheme for salary increments for all of the RSPCA’s 1,700 staff.
Third Sector understands that if an agreement with the union cannot be reached, staff will be dismissed from the charity if they do not sign the new contracts by 31 March next year.
In a newsletter update issued to Unite members at the RSPCA on Monday after two sets of talks, the union said the charity "has not provided anywhere near enough detail to enable your union to enter into meaningful negotiations".
It added: "Your union feels that the society is deliberately employing an information drip-feeding process to eat up negotiation time and that it intends to impose changes to employee contracts without agreement."
The update said the talks "have been deliberately set up to fail".
The charity rejected these claims.
The union said a snapshot poll of its members showed 67 per cent were prepared to take industrial action over the issue.
It said it had warned the charity that "if the society continued with their current negotiating strategy, the meetings will inevitably end in failure" and "the whole process is being deliberately rushed".
Jesika Parmar, regional officer at Unite, told Third Sector that the talks had been "designed to fail in a most cynical fashion".
She said the union had called on the charity to honour the previously planned incremental rise, which was due to take place in April, and to extend the negotiation period to allow for "full and meaningful discussions".
She said: "That decision currently sits with the chief executive, Chris Sherwood, who is due to make a decision on Friday 1 November.
"A snapshot poll of our members shows that two-thirds of them would be prepared to take part in a ballot for industrial action, including strikes. We hope that it does not come to that, but the ball is very much in the management’s court if it wishes to recalibrate employment relations in a more positive way."
The union said it had "hundreds" of members at the RSPCA and described its membership as "angry and growing", but declined to clarify exactly how many members it had.
An RSPCA spokeswoman told Third Sector the charity was "very hopeful" it would "reach a solution which everyone can agree with" through "consultation and constructive discussion".
She said: "We do not accept the negotiations are set up to fail nor that we have not provided enough information to Unite. We want to work with Unite, as well as with the majority of employees who are not members of the union, to deliver a fair pay and reward framework that ensures the RSPCA is on a sustainable financial footing.
"Our proposals are well thought through and the timetable for talks represents our desire to give certainty to all employees as quickly as possible."