The Premier League's rock-bottom side have eight players out of contract and five loanees due to return to their parent clubs at the end of the season.
Mannone's deal does not expire until 2015, though, and Poyet believes that it could be September before the Italian keeper enters negotiations.
"I think Vito knows that we've got eight who are out of contract and loan players, so he'll have to wait until September," he told the Sunderland Echo.
Jack Colback and Phil Bardsley are reportedly the only players to have held contract talks since Poyet's arrival in October, although the Uruguayan has already expressed his belief that the duo will exit the Stadium of Light.
And it now looks unlikely that any of the remaining out-of-contract players will stay for next season, with Poyet adding: "We had our intentions (with out-of-contract players) and they didn't work out.
"We've stopped now and there's no more talks with anyone."
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