Palace – along with Premier League rivals Bournemouth, Swansea City, Stoke City and West Bromwich Albion – have been mooted as a potential next destination for Terry after it was announced this week he will call time on a trophy-laden 22-year spell at Stamford Bridge and look to continue his playing career elsewhere after acknowledging that regular opportunities under Antonio Conte "will be limited" moving forward.
The Times subsequently reported that a reluctance to leave his home in the Surrey village of Oxshott could make the Eagles and Bournemouth favourites to secure Terry's signature, with Allardyce said to be a "huge admirer" of the veteran defender.
However, speaking ahead of Sunday's (23 April) trip to Liverpool, the Palace boss highlighted the strength and depth of his current defensive options and claimed that centre-back may not be an area that he looks to further reinforce at the end of the season.
"I have Scott Dann, James Tomkins, Mama Sakho, Damien Delaney and Martin Kelly," he told reporters at a pre-match press conference, as quoted by football.london. "So actually central defence-wise, we're looking pretty secure in that position at the moment so I'm not sure that's going to be a position we actually need [to strengthen in] if and when we're safe. And hopefully we are safe by the end of the season.
"But that position looks pretty healthy from the number of players that we do have in that position. So I'm not so sure that John, as fantastic as a player as he is, yes he'd do us a great job but with those amount of centre-halves already at the club I can't see that happening at the moment."
Palace's interest in Terry is seen as a potential contingency plan to be pursued in the likely event that they are unable to complete a permanent deal for Liverpool loanee Mamadou Sakho. The French international has thrived since arriving at Selhurst Park in January, playing an instrumental role during a run of five victories in seven matches that has seen the club pull seven points clear of relegation.
Reiterating his desire to sign the player, a cautious Allardyce, said: "Our first priority is we have to make sure we're safe as quickly as possible. Would we like Mama Sakho? Yes. Would we talk about it now? No. Because we're not safe. When we're safe we'll maybe talk about it then and many other players."
Sakho is unavailable to face his parent club at Anfield this weekend, although James Tomkins and Chelsea loanee Loic Remy are both set to return from respective calf injuries. Scott Dann, Pape Souare and Connor Wickham all remain sidelined.