Simeone is the most successful coach in Atletico's history, winning eight trophies since his arrival in 2011, and will reach a record 612 games in charge of the club on Saturday.
Atletico, fourth in LaLiga on 41 points, will look to close the 10-point gap to second-placed Real at the Bernabeu.
Ancelotti, who has won nine titles in two spells as Real Madrid manager, admitted he would like to spend time with Atletico's Argentine coach and share their knowledge.
"I like him as a person, he is very honest in his game evaluation," the Italian told reporters on Friday.
"He has been very successful with Atletico, a lot of the success of his team has been thanks to a coach who has been able to bring in a very recognisable mentality and identity.
"I would like to spend time with him because we love football. I think he has nothing to learn from me. I would like to see how he prepares for tomorrow's game. We can share this after the game."
Earlier on Friday, Simeone thanked the players he has managed at Atletico saying they are the reason he can achieve his historic numbers and results.
"I am fortunate, I have to be grateful to the club and to all those who have played for the team," Simeone told a news conference.
"The numbers go hand in hand with the results. I'm in the place I want to be and I still have a lot of hope."
Since the World Cup break Simeone has led his team to eight wins in 12 games and a run of six unbeaten LaLiga matches.
Despite Atletico being far from contention for the league title, with Barcelona 18 points ahead of them, he said his team's enthusiasm and motivation will not wane.
"You have to compete every game. There are seasons where we can compete to win something and others where it seems a long way off," Simeone said.
"As a club fighting in a competition is very good for us to continue to grow. Every game that we put on the red and white (jersey) we have to be excited."
