There has been little love lost between the pair since they had a clash of style and words when they were managers of Blackburn and Liverpool respectively. Benitez had sarcastically suggested Barcelona were looking at imitating what he felt was Blackburn's robust style, while Allardyce said:
"He's got personal with it for many, many years now. That's why I don't like him and the feeling is probably mutual."
The feud started when Allardyce felt Benitez had made a 'game over' hand gesture when Liverpool went 2-0 up against his Blackburn side in 2009. However, as he prepared his team to face the European champions in Saturday's lunchtime kick-off, Allardyce is was not interested in going over old ground.
"I don't want to jump into that scenario, I am a bit bigger than that, I don't want to go tit for tat," said Allardyce.
"It was a long time ago, a lot of water has gone under the bridge since then and I am just looking forward to the game.
"All I do is look to compete at a level going against not just Chelsea, but also against a man who has a real good record, to see if we can upset them."
Benitez has yet to win over the Chelsea fans, who roundly booed the former Reds boss ahead of his opening game in charge at Stamford Bridge against Manchester City, which ended goalless. Chelsea again drew a blank in the midweek west London derby with neighbours Fulham. Allardyce, however, insists there can be no thoughts of it being a good time to tackle the European champions.
"I would say not because in the last two games they have not conceded a goal. At the heart of every good side is producing a clean sheet," he said.
"Rafa has already sorted out what was a problem under (former manager) Roberto (Di Matteo), and now they have got a couple of clean sheets in a row, so it will not be long before they can turn that into a victory if they continue to defend like that.
"It will be more difficult to break Chelsea down than it would have been, chances will be few and far between."
Allardyce maintains once the Blues are back to winning ways, the boo-boys will soon be appeased. He continued:
"At Chelsea, like any other club, it is all about winning. I am sure once Rafa starts winning, then that will change, when the team starts winning then supporters get behind everybody.
"It takes time to adjust to the ideas of a new coaching regime, that is always the case.
"Over the last few years, Chelsea players have been used to it because they have had a quite a few changes."
West Ham lost 1-0 at Manchester United on Wednesday night, but gave a good account of themselves against the Premier League leaders. Allardyce will have midfielder Mark Noble available again following suspension, while on-loan striker Andy Carroll will be assessed after picking up a minor knee problem. The Irons have produce some solid results on their return to the top flight, moving up into the top half of the table. However, Allardyce knows his injury-hit squad will need all of their resilience to avoid a third straight defeat this weekend, having also lost at Tottenham.
"Every man needs to continue to put the shift in they are doing to try to get a result," he said.
"While we have lost two games back-to-back for the first time, when you look at the size of the teams they are against, I don't think there is any reason for the players to lose confidence
"The key issue for us is to try to get some points on the board as quickly as possible in this difficult run of fixtures."