The former England manager believes the West Ham United boss wouldn't turn down the chance to get one over on his old club.
The Magpies sit just two points clear of the relegation zone after a run which has seen them lose eight consecutive games and become embroiled in a basement battle, something they had previously looked to be clear of.
In contrast, the Hammers sit comfortably in ninth place in the table after an impressive first half to the campaign. Both sides meet on the final day of the season, and Hoddle believes Allardyce would love to relegate his old side given their acrimonious history.
“Can you imagine if it goes to the wire, the very last game and Newcastle have to beat West ham to stay up?” he said.
“Now that will be a scenario that Sam Allardyce will relish! What a game that could turn out to be, with plenty of history surrounding Sam in that game, for sure.”
The former England manager also says that John Carver’s side would have nobody to blame but themselves should it come down to the last game in their bid for survival.
The club looked well clear of the relegation dogfight under former boss Alan Pardew, but his departure to Crystal Palace saw Carver take over as caretaker manager and their slide down the table has been alarming ever since.
The majority of the squad look like they have switched off for the season as well, and Hoddle says it would be their fault should relegation still be a prospect come the season finale.
“Newcastle only have themselves to blame if it comes down to the last game to survive,” he added.