Mr Ecclestone, 85, is understood to have offered to pay for a private security firm to track down Aparecida Schunck, the mother of the mogul’s wife, Fabiana Flosi, who was abducted from her home in Sao Paulo more than a week ago.
According to reports the Formula One boss also wanted to fly to Brazil to assist police, but was told doing so may have harmed their efforts.
The 67-year-old was rescued from a flat on the outskirts of the city on Monday without any money being paid to her kidnappers.
Shortly after Ms Schunck was reunited with her relatives Mr Ecclestone said “The last few days haven’t been very good. This isn’t a good thing to happen to you and your family,” he told the Mail Online.
“The police officers we dealt with were fantastic, they did an unbelievable job, it was absolutely first class. We are very, very, very happy with them.”
Investigators from Brazil’s elite anti-kidnapping unit are probing allegations that a helicopter pilot who had worked for the Formula One boss was linked to the plot.
Jorge Eurico da Silva Faria, who works for Ecclestone in Brazil, was one of three men arrested in connection with the kidnapping, said police.
A spokesman for Sao Paulo police said da Silva Faria was arrested “red-handed” with two other men, Vitor Oliveira Amorim and David Vicente Azevedo.
“The investigation continues and the police did not rule out the involvement of other suspects,” he added.
It is believed investigators monitored phone calls between the family of Ms Schunck and the captors, tracing them to the location where she was being held.
She was not harmed in the operation conducted by Sao Paulo’s anti-kidnapping division.
Speaking after she was freed Ms Schunk said: “I just ask that the crooks do not kidnap anyone else in Sao Paulo because they will be arrested”.
Brazilian magazine Veja had reported that the ransom for Ms Flosi’s mother had been demanded in pounds sterling and divided into four bags of cash.