Allardyce has endured a frustrating transfer window, with Jeffrey Schlupp his only signing to date despite hoping to land multiple defensive reinforcements.
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But he will not concede defeat for Jenkinson amid reports a deal for the Arsenal full-back has broken down over personal terms, while the club are still keen on Van Aanholt after having an initial bid rejected by Sunderland.
Veteran Juventus defender Evra has also been linked with a move, but there is no progress in that pursuit either.
“Until the chairman rings me to say the Jenkinson deal is dead, it’s still on for me,” Allardyce said ahead of Saturday’s match against Everton.
“The same with Van Aanholt - we are interested and in this window you never know what might happen.
“[There is] no progress [with Evra] at this moment in time. We have got one signing, but missed about 20. We missed one yesterday in Jake Livermore. We’ve not much success so far.
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“There is nobody for sale unless the bid is something we can’t afford to turn down. Jeffrey Schlupp is available for selection.”
Palace are struggling down in 17th position and are only out of the bottom three on goal difference having failed to win in seven top-flight matches.
