Lawyers representing the mother and daughter are to seek damages for "pain and suffering". They alleged that Disney World was reluctant to involve police after the assault.
They have also claimed that Disney accidentally contacted the man jailed for the sex offence and asked him to re-apply for work.
Jeffrey Bise was jailed for 21 months after admitting to the assault on the girl in January last year. He was working for a company licensed to sell puppets at Disney World when he committed the offence. While attaching a puppet around the waist of the girl, Bise put his hand up the girl's skirt and molested her three times.
The mother, who lives in England but is not being identified, was on her first trip to the United States with her daughter, son and uncle, who is a British police officer.
While Bise was awaiting sentence, Disney sent him a brochure inviting him to apply for a full-time position, according to information shown this evening on ITV's Tonight with Trevor McDonald. The brochure stated: "The Walt Disney World family is always looking for ways to reach out to potential Cast Members like you who want to make friends, make magic and make a difference."
While the lawyer representing the mother and daughter conceded that this was an accident she argued that it showed the lax vetting system operated by Disney.
Mary Ann Morgan, an attorney in Orlando, Florida, said that she intended to file a lawsuit in about a month. She said she was planning to claim damages from the puppet company and Disney. "The employer has a vicarious responsibility for the acts of their employees," she argued. She said she would be asking for "damages for the child's pain and suffering".
She claimed that Disney waited an hour after the assault was reported before calling the police, and then only after the family insisted.
The mother claimed that after the attack Disney offered the children an autographed picture of Minnie Mouse and a Minnie Mouse mug in way of compensation. They were also offered a breakfast with Minnie and Mickey Mouse, which they refused.
A statement from Disney said: "The Orange County Sheriff's Office was called in and handled the case. The parents of the child did not want to press charges at the time and ultimately the local state attorney pressed forward with the case."
The mother has said that she did want a prosecution.
Disney said that it does run criminal background checks on all new staff and regularly screens all its staff against Florida law enforcement's database of sex offenders.