The LSE Group is in the late stages of a pitch following five years with Citigate, which is understood to have declined to repitch. It is understood that the new brief includes a public affairs element.
One agency figure said that the company would be looking to "portray itself as the future of the City of London, and portray the place that it has within UK plc internationally", and convey its growing global clout as it diversifies.
Aside from the London Stock Exchange, the group owns assets including the Italian Stock Exchange, Borsa Italiana; European fixed income market, MTS; and pan-European equities platform Turquoise.
News of the pitch comes as the London Stock Exchange looks ahead to increased activity amid brightening economic prospects, with some reports pointing at up to 100 IPOs this year.
Both Citigate Dewe Rogerson and the LSE, which has also put its work with auditor PricewaterhouseCoopers out to tender, declined to comment.