Midfielder Colback, 24, and defender Bardsley, 28, have both rejected new deals at the Stadium of Light and, with their current contracts due to expire in June, the pair will soon become free agents.
"Everybody knows we have been in contract talks with a couple of players, but at the moment everything is on standby," Poyet told reporters. "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. To be honest, it doesn't matter where we finish - I cannot see them staying at the club."
Colback came through Sunderland's youth system and has so far made 129 first-team appearances for the Wearside club. Meanwhile, Bardsley, who joined the Black Cats from Manchester United in January 2008, has featured 157 times.