"That's the chairman's responsibility," Allardyce told the reporters when asked whether he will be able to retain Zaha.
"Spurs were always mentioned because agents or somebody decided to stir the pot. We all know who stirs the pot, behind the scenes, who do it, even though they deny it, but we know they do it."
Allardyce also asked for match officials to be extra vigilant when refereeing Zaha, suggesting the 24-year-old was targeted by opposing defenders on a consistent basis.
"He (Zaha) gets terrible treatment... because he's so skilful. Maybe he needs a bit more protection from the referees," the former Bolton, Newcastle and West Ham manager added.
"He's got to realise that's down to his genius ability that these lads can't cope, and because they can't cope, they've got to end up fouling him."
Palace, 16th in the league with 10 games to go, have reeled off three consecutive victories to move four points clear of the relegation zone.
(Reporting by Hardik Vyas in Bengaluru)
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