The deals of the Scottish defender and English midfielder expire this summer and Poyet insists the club is working hard to secure the services of the key duo.
"We started negotiations a few weeks ago now. The situation with the negotiations has changed a little bit, because there's another person in charge - now that Roberto De Fanti has departed," he told The Journal.
"Let's hope. It's important not to be too aggressive in terms of the contract because of the position we're in, and of course you need to be realistic. They'll say 'Let's wait, let's see where we finish'. It works both ways."
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