Last season's 0-0 draw between the sides at Stamford Bridge drew stinging criticism from Mourinho, who brandished Allardyce's approach as "football from the 19th century".
However, West Ham head across London this time sitting fourth in the Premier League table after a superb season thus far, which has seen Allardyce implement a new attacking style in the team.
With a home clash against Arsenal to follow in the hectic festive schedule, Allardyce is looking forward to the challenge of proving his side's top-four credentials.
He said: "We have obviously improved tremendously from where we were, but that doesn't make it any easier for us playing Chelsea at Stamford Bridge because of the force that they are, and because of the manager that he [Mourinho] is.
"He is probably the best working club manager in the world at the minute on his track record. I don't think there is any doubt about that.
"There is probably only Carlo Ancelotti that perhaps matches him, but certainly what he has done in his time across many different countries has been outstanding and that's why I was glad to have him back.
"I want to pit my wits against the best and obviously he is proving that again here in England with Chelsea this season.
"We've got the two hardest games over 48 hours over Christmas.
"Chelsea away and Arsenal at home in the space of 48 hours is a big demand for us, even though we're on top of our game at the moment.
"Getting through these two games is going to be a tremendous effort for all the players selected, and hopefully they'll come through for us as they have done for most of this season."
