It is understood no formal deal has yet been struck, but talks between the two companies have taken place through an intermediary consultancy.
Such a move would see JWT aiming to mirror the success it has had with the acquisition of Cheetham Bell in November 2000, which was subsequently merged with JWT's office in Manchester. Simon Bolton, the JWT chief executive, is thought to be leading the talks.
Any acquisition would have to meet WPP's strict financial performance and growth targets to be approved.
Leith's Edinburgh-based clients, such as its Coors Brewers business and Standard Life, would plug gaps within JWT's client portfolio.
However, any deal being discussed by the parent agency in Scotland, under the auspices of its chairman, John Denholm, and chief executive, John Rowley, would need to be agreed by the management at Leith London. The London operation operates on a semi-autonomous basis, including having a client list largely separate from the Scottish office.
At the launch of Leith London in October 2000, the founding partners - who included Jeremy Pyne, John Messum and Paul Silburn - are believed to have been given the option of equity in an enlarged holding company consisting of both operations, called Silvermills Group.
Depending on whether performance targets were met, the founders were in line to control up to a quarter of The Leith Agency.
WPP referred enquiries to JWT, and JWT refused to comment. Management was unavailable for comment at Leith's offices.