Saints and Millwall were this week linked with the 20-year-old, who came through the ranks at Selhurst Park and has been a regular in the first-team squad this term.
But Burley, a former Southampton manager, told the South London Press: "He is under contract and has been offered a new one. We've had no interest."
Cadogan has started seven Championship matches for the Eagles and scored two goals.
Source: PA
Source: PA