The England international will be allowed to leave the Emirates this month and a move to Palace appeared to be his most likely destination.
Arsenal stars continue injury comebacks in training
Wed, January 18, 2017
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However, speaking ahead of Palace's match with Everton this weekend, Allardyce was refusing to give up deals for Jenkinson and Sunderland's Patrick Van Aanholt.
"Until the chairman rings me up and says Carl Jenkinson deal is dead, it's still ongoing for me," said Allardyce.
Carl Jenkinson could still join Crystal Palace
"The same with Van Aanholt – we're interested."
Allardyce knows both players very well having worked with Jenkinson at West Ham and Van Aanholt last season.
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Sam Allardyce is desperate to bring in new players
The ex-England manager is desperate to bring new players to Selhurst Park but says the club have failed to sign around 20 players in the window so far, including new West Brom midfielder Jake Livermore.
He added: "We've got one signing, but missed about 20.
"We missed one yesterday in Jake Livermore. Not much success so far. We were in the race and we didn't win that race."