Terry will be a free agent once his contract at Stamford Bridge expires this summer and a host of clubs both at home and abroad have already been linked with the 36-year-old following his announcement that he will leave Chelsea.
However, Allardyce believes that other areas of the team need strengthening more than central defence, and the former England boss is also likely to prioritise signing Mamadou Sakho on a permanent deal should he look for defensive reinforcements.
"I'm not sure if that's going to be a position we'll look at 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 the players we have.
"I'm not so sure that John, yes, fantastic player that he is, yes he'd do us a great job, but with those amount of centre-halves at the club I can't see that happening at the moment."
The likes of West Bromwich Albion, West Ham United and Swansea City have also been credited with an interest in Terry.