Chilean cruise worker Fabian Zanzi claims that the Pulp Fiction actor offered him $12,000 (£7,500) for sex.
Speaking on Chilean news show Primer Piano, Zanzi alleged: "He said that I had something on my neck. I thought it was lint.
"When he got close to me, he took off his white robe and he was naked. He hugged me and asked me to give him a massage."
However, the New York Post says Zanzi is yet to file a lawsuit agains Travolta, despite his claims otherwise.
The two other plaintiffs are represented by Pasadena, California attorney Okorie Okorocha and have remained anonymous, seeking $2 million (£1.2 million) in damages each.
Travolta's lawyer Marty Singer has strenuously denied both claims, suggesting he will launch a counter-suit for malicious prosecution.
The 58-year-old himself released a statement through his publicist saying he was over 2,000 miles away while the supposed incident occured.