Rangers centre-half Hendry and Celtic midfielder Burley failed to agree personal terms with derby boss, Jim Smith.
"The situation is that we've made bids for the two players that were accepted," Smith said. .
"He put certain suggestions to us and we felt we had gone as far as we wanted to go.
"It's pretty much a similar thing with Colin really. It's a clause we have in every contract that he wasn't happy with. We stick by it; we can't change it for any player.
"To be fair, we didn't mention it in the early stages but they moved their goalposts three times; we only moved ours once.
"It's a big blow but we've got to feel right about everything and the thing that's most important to me is the support of the chairman and the board, who allowed me to go for two top Scottish internationals."
The news is another setback to Smith on the eve of their home Premiership clash with Manchester United, with more than half-a-dozen of his first side out.
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