Carlo Ancelotti described Pep Guardiola as "a genius" - despite admitting Manchester City's levels have dropped since last season - as he prepares to take his Everton side to the Etihad Stadium.
Former Chelsea and Real Madrid boss Ancelotti has overseen victories in both of his matches in charge of the Toffees since taking over from caretaker manager Duncan Ferguson, but he said facing the champions on New Year's Day would be a stern test.
Third-placed City are 14 points behind Premier League leaders Liverpool after suffering two defeats in their last five league outings, but Ancelotti said he still regards Guardiola as a master of the game.
"Pep is a fantastic manager," Ancelotti told reporters. "I have a good relationship with him.
"We met some times, not a lot in games, but at some conferences in Italy. I have a good relationship with him and a lot of respect for his job.
"He is, at a certain point, a genius because he has always tried to do something special on the pitch.
"City are maybe not on the level of last year but they remain a fantastic team with fantastic players and a fantastic manager, so for us it will be really, really tough to compete with them but we need to have the confidence and focus on our football.
"Against City will be a fantastic test for us to see where we are in the sense that it's a really strong team but we have confidence to do our best. It's good to have this kind of test. We have to be happy to compete with the best teams in England and in Europe."
Everton beat Burnley 1-0 at Goodison Park in Ancelotti's first game in charge and then won 2-1 at Newcastle United, with Dominic Calvert-Lewin scoring all three of the Toffees' goals under the Italian.
Asked whether he would seek to improve his squad when the transfer window opens in January, Ancelotti said he would wait until after Everton's FA Cup clash with Liverpool on January 5 before speaking to the club's board.
"The market is not open yet," said the 60-year-old.
"There are a lot of rumours, that is normal. Everywhere in the world is like this, Italy is the same. We are not looking in this moment.
"After the fifth of January I'm going to have a meeting with the club and we can talk about if it's possible to try to improve the squad. In my opinion it's a good squad.
"Some players I didn't know very well but we've started training together and I know them better."