Both Colback and Bardsley are out of contract at the end of the season, and both have been instrumental in Sunderland's resurgence in the league, while also playing an important part in getting the club to the Capital One Cup final.
Poyet told The Journal: "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.
"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."