Senna: Died in Formula One crash in 1994
The film will focus on the time leading up to Senna's fatal crash, and could even reveal new information about the crash itself, according to the Observer newspaper.
Spanish actor Banderas, known for roles in Desperado and The Mask of Zorro, has led the project about the Formula One legend.
Banderas and other film-makers have been working closely with Senna's family, and a deal to bring the story to the big screen is close, the paper says.
"There are a lot of things people know," Senna's older sister, Viviane, told the paper.
"But there are also a lot of things that people don't know and that only the family can reveal.
She said family members are the only people who can tell the story of many things that remain unknown.
"Antonio Banderas wanted us to collaborate and bring that side of things to light - all that Ayrton saw and felt, both on and off the track."
Banderas, who has also starred in Evita and Spy Kids, has said he got the film rights from Senna's family.
Accusations
"This character was tormented and having a bad time and predicting that he was going to die," he has told Australian website Urban Cinefile.
Senna, a three-time world champion, died when his car crashed into a concrete wall during the San Marino Grand Prix at Imola in 1994.
Three members of the driver's Williams team were cleared of manslaughter amid accusations that safety concerns had been ignored to make the sport more exciting.