Sheffield Wednesday manager Brian Laws says talks with Tommy Spurr and Richard Wood are on hold.
The defenders are yet to sign new contracts but Laws says the players are "core to his plans."
Laws told the club's official website that discussions were expected to resume at a later date.
"Everyone is happy to leave this until later this year, at which point we hope to have seen a conclusion regarding the club's investment process."
Wednesday offered a contract to trialist Ryan France but say he will now sign for another club.
Laws added: "Ryan did very well in the games and in training, but there was always a concern about his knee and this was one of the reasons why we took our time with him. I wish him all the best wherever he goes."
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