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The youngster suffered severe burns after the attack at a Home Bargains store in Worcester, West Mids, after he was covered in the corrosive liquid.
Officers believed that the child was deliberately targeted when the investigation was launched.
Now it has been reported that the mother of the boy, who is thought to be Eastern European, had been hiding in a safe-house after a fractious break up.
The MailOnline reported that the police are now probing into whether this was a targeted hit on the child or his mother.
Three other men were arrested in London on conspiracy to commit grievous bodily harm. They were aged 22, 25 and 26.
A fifth man, aged 41, has also been arrested on suspicion of conspiracy to commit grievous bodily harm.
The Express reported that the boy was left screaming in agony and with serious burns to his face and arm when the incident happened at 2:15pm on Saturday.
He was treated in hospital and has now been discharged with injuries to his face and arm. There is no certainty of whether his injuries will be long-term.
The MailOnline reported that West Mercia Police confirmed the relationship between the father and son and a source said: "He is still in custody. No charges as yet have been brought. This is an ongoing investigation."
It is now believed that the mother and her son have now been moved into a police-designated safe house amid fears they could be attacked again.
A new neighbour told the MailOnline that she had been living with the toddler and her two other children in a secluded residential street in Worcester after fleeing the family home in Wolverhampton because of 'difficulties within her relationship'.
Another neighbour said there had been 'bad blood' caused by a family dispute and said the attack may have been launched over the end of a relationship with the three-year-old's mother, who could have been the true target.
A source close to the investigation told the MailOnline: "She had moved to Worcester from elsewhere but hasn't been here long. She had moved because of difficulties within her family.
"Nobody knows her really well and she didn't have any connection with Worcester. That's why she was moved here, because she was fleeing her previous situation.
"Somehow the parties she was in a dispute with found out where she had moved to and that's how this horrendous incident has happened.
"The acid attack was targeted at her. The child just happened to get in the way."
The investigation is ongoing.
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