Terry, 36, is leaving the Blues after over 18 years in the first-team squad when his contract expires.
But Palace are not going to be in the race for his signature, even though Swansea City have indicated they may be interested while West Ham boss Slaven Bilic refused to rule out the prospect of making a free transfer move.
"I have got Scott Dann, James Tomkins, Mamadou Sakho, Damien Delaney and Martin Kelly, so actually in central defence we are looking pretty secure," Allardyce said.
"I'm not sure if that's going to be a position we will look at if and when we are safe, and hopefully we are safe by the end of the season.
"But that position looks pretty healthy from the number of the players we have.
"I'm not so sure that John, yes, fantastic player that he is, yes he would do us a great job, but with those amount of centre-halves at the club I can't see that happening at the moment."
Allardyce also confirmed that centre-back James Tomkins and forward Loic Remy are both available to face Liverpool on Sunday at Anfield.
The Palace boss is pleased with the timing of Tomkins' availability, with on-loan Liverpool defender Mamadou Sakho, who has been on fine form, ineligible to play against his parent club.
Remy has struggled with a number of muscular injuries this term, making just seven appearances in all competitions, while Tomkins returns from a calf injury after three games out.
"We have a few back out there training with us that haven't been available in recent weeks which is ideal with a congested fixture period coming up," said Allardyce at his pre-match media conference.
Palace have been in fine recent form in the Premier League, collecting 16 points from their last seven games, with the 3-1 loss away at Southampton the only defeat in a run that included victory at Stamford Bridge against league leaders Chelsea and the 3-0 humbling of Arsenal at Selhurst Park.
"We are in Champions League form for picking points up, which should give us a huge amount of confidence on Sunday," said Allardyce.
"Hopefully we can be good enough, big enough and brave enough, and confident enough to try and repeat what we have done against Chelsea and Arsenal recently."