Shanghai, who are ninth in the Chinese Super League, fired Frenchman Tigana in April after a poor start to the season, replacing him with interim coach Jean-Florent Ibenge.
"I hope that Shanghai Shenhua will be the best. There is perhaps no one word to describe my hopes," Batista, with the help of a translator, told a news conference.
"Perhaps the current situation of the team is not too ideal, but overall I think we will do something important and have a good result.
"This project is a challenge for me so I will do my best to win the league. But it is also a gamble. I believe if we do our best, we can do it," the 49-year-old added.
He was sacked after only a year following Argentina's failure to end an 18-year wait for a major title at the 2011 Copa America.
But former Argentina midfielder Batista, who has the option of a one-year contract extension, said Anelka was a key part of the club's future and they already got on well together.
"First of all, I have a good relationship with Anelka. We have had good communication during the past few days. So we have been talking and, as a player, Anelka plays a very important role," Batista said.
"He can bring a level of experience to help this team. Also, he has been very welcoming of my arrival."
Shanghai have been strongly linked with a move for Anelka's former Chelsea team-mate Drogba, who has announced that he is leaving the Champions League winners at the end of June.
"My initial thought is to bring Drogba to the club. He is a very good player and we will welcome him here... I very much hope that Drogba can join us," he said.
League leaders Guangzhou Evergrande this month appointed Italy's former World Cup-winning coach Marcello Lippi after sacking South Korean Lee Jang-soo.
