The pair come off contract in June.
"Everybody knows we have been in contract talks with a couple of players, but at the moment everything is on standby," said Poyet.
"Everyone is responsible for their own decisions and I don't think we are in a position to push people to do things they do not want to do.
"I'm not stupid, I understand it brings uncertainty to the club for the future.
"We have only offered contracts to two of the eight out-of-contract players, and now those negotiations have both completely stopped.
"To be honest, it doesn't matter where we finish - I cannot see them staying at the club.
"It would be too easy to make a decision based on where we are [Premier League or Championship] because it would be very unfair on the fans."