The Senegal international was reported to have signed a three-year deal worth 16 million euros ($17.9m), Xinhua news agency said on its website, after the Shanghai club confirmed the 30-year-old would be joining.
The figure would eclipse the previous CSL record of 15 million euros paid in January by champions Guangzhou Evergrande for Brazilian Ricardo Goulart.
The Shanghai club did not confirm the figure, Xinhua added, referring to a “possible record transfer fee”.
Shanghai Shenhua — who are sometimes called Shanghai Greenland Shenhua — did not reveal any financial details in a statement released on its website Saturday announcing Ba’s arrival at the club.
Ba, who will undergo a medical on Sunday, made the switch to China from Turkish first division side Besiktas, where he scored 27 goals in 44 games last season, the statement added.
The journeyman striker, who also played for West Ham United and Newcastle United in the Premier League, had been tipped for a return to England. West Bromwich Albion were understood to be the leading contenders for his signature.
But he will instead line up alongside former Everton star and Socceroo Tim Cahill and Mali international Mohamed Sissoko, who arrived in China from La Liga side Levante after spells at Paris Saint-German and Liverpool.
Ivory Coast veteran Drogba — who left Chelsea on a free transfer at the end of last season — and his former teammate at Stanford Bridge, Nicolas Anelka, both played for Shanghai.
The CSL is now among the biggest spenders in world football leagues. It was second only to the Premier League during the recently closed winter transfer window, according to statistics from German website transfermarkt.
It is also currently the highest-attended football league in Asia.