The unnamed professional player began proceedings at the High Court this week, accusing Twitter of releasing details that should have remained private under the terms of a court order.
"An application has been made to obtain limited information concerning the unlawful use of Twitter by a small number of individuals who may have breached a court order," law firm Schillings said in a statement emailed to Reuters on Saturday.
Schillings said it was not suing Twitter on behalf of its client. No one at Twitter immediately responded to a Reuters request for comment.
Attempts by British celebrities to keep aspects of their private lives secret using strict court orders have been undermined by Twitter users posting allegations on the website.
Newspapers and some politicians have criticised the use of so-called "super injunction" court orders that stop the media from publishing a story and even the fact that the ban is in place.
Critics say the courts are being used to stifle freedom of speech and shield famous people from scrutiny. Those in favour of the court orders say they protect people's right to privacy.
Lawyers say that Twitter, as a US-based organisation, would be hard for British courts to pursue.
"But it shouldn't put the person involved off taking action to find out the names of the perpetrators because that is the only way of giving effect to English law," said lawyer Mark Lewis of Taylor Hampton Solicitors.
"If you just picked on 20 tweeters who've got embroiled in a legal dispute with lots of costs and possible imprisonment or fines for breaching an injunction, other tweeters would think long and hard before they started doing that themselves."
