Finsbury was appointed to the brief following a competitive pitch.
Earlier this month, Sky News reported that Worldpay owners Advent International and Bain Capital were close to appointing Bank of America Merrill Lynch, Goldman Sachs and Morgan Stanley as global co-ordinators of an IPO that could happen as soon as this year.
It would be among the biggest IPOs on the London Stock Market in recent years and see the company enter the FTSE 100. Sky News estimated the valued of the company to be between £5.6bn and £8bn, based on flotations involving similar firms.
Worldpay, which generated revenue of £3.65bn in 2014 and handles 26 million transactions each day across more than 40 countries, is also reported to be looking at New York equity markets as an alternative. In addition, it is understood that a trade sale has not been ruled out.
The company, who clients include Sony and Google, was sold by the Royal Bank of Scotland to Advent International and Bain Capital for £1.7bn in 2010.
Worldpay also works with Golin for some of its corporate PR work, and this relationship will be unaffected by Finsbury’s appointment.
Worldpay has declined to comment on reports of its planned IPO.