A successful swoop for Batista would come after 2006 World Cup-winning Italian coach Marcello Lippi took charge of rivals Guangzhou Evergrande last week.
"The contract has not been signed so far. The two sides (Batista and the Shenhua Club) are still in negotiation," Ma Yue, the club's spokesperson, said.
Batista coached Argentina to Olympic gold at the 2008 Beijing Games before replacing Diego Maradona as the coach of the national side.
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.
Shanghai fired Frenchman Tigana in April after a poor start to the season, replacing him with interim coach Jean-Florent Ibenge.
French striker Nicolas Anelka, who joined Shanghai from Chelsea in January, will continue to combine playing as well as helping to coach the side.
Anelka's former striker partner Didier Drogba is still a possible target, though the Ivorian's heroics in helping Chelsea win the Champions League could earn him a new deal in London.