Malcolm Gooderham, the founder of TLG, is expected to join FTI along with the acquisition.
The two parties were still hammering out details at the time of publication.
Although FTI has frequently been tipped to make an attempt to strengthen its public affairs offering in recent years, its interest is mainly in the thought leadership capability of TLG.
TLG set up media arm TLQ a year ago, launching a quarterly digital magazine also called TLQ, which Gooderham likened to "TED meets Harvard Business Review".
Public affairs is understood to make up a third of TLG’s business. Its PA clients include Yorkshire Water, Serco and Prudential, according to the register kept by the Association of Professional Political Consultants.
FTI’s former incarnation Financial Dynamics bought New Labour lobbying outfit LLM in 2005, but the brand name was dropped in 2008 following a number of senior departures.
In 2011 FTI came close to acquiring Portland, but the deal fell through and Omnicom bought the public affairs agency in 2012.
Gooderham launched TLG after quitting Weber Shandwick in 2007, going on to win a PRWeek Award for best new agency and picking up clients such as Nestlé, Asda and Kingfisher.
FTI Consulting and TLG Partners declined to comment.