Bolton recorded some notable results against Arsene Wenger's team during Big Sam's Trotters tenure, with the most memorable arguably being a 1-0 victory over the north London club in the 2006 edition of the FA Cup.
"I enjoyed beating Arsenal more than anyone when I was in charge at Bolton. We'd really got to them and Arsene Wenger hated us,” he said.
"Of course, Arsenal beat us sometimes, but we drew with them or beat them more often than expected and Wenger couldn't handle it."
Allardyce recalls how, on one particular occasion after the Lancashire club claimed a draw at Highbury, Wenger would refuse to shake hands with the Bolton manager.
He also claimed that the Frenchman would often attempt to influence referees through the media by creating the perception that Bolton were a team of bullies.
"He's a fantastic manager, I cannot deny that. But the more I could wind him up, the more I liked it,” he added.
Allardyce will come face-to-face with Wenger at the Emirates in December, with Sunderland travelling to Arsenal having claimed a 0-0 draw on their last visit to north London.
That result secured the Black Cats' Premier League status for another year, last season, and a similarly positive result could be required this time around.