Corporate partner Stephen Blackshaw and capital markets partner Richard Levy led the Linklaters team acting for Yorkshire on the deal.
Financial services partner Adam Bennett led an Addleshaws team for longstanding client Chelsea, with banking partner Mark Thomas also on the deal.
Discussions on the deal are said to be at an advanced stage. It would create an asset with a value of around £35bn and cement Yorkshire’s place as the UK’s second largest building society.
The merger will also see Chelsea use contingent convertible notes - or CoCos - as part of the deal. These notes were used in Lloyds Banking Group’s record-breaking £22.5bn capital raising exercise last month.
The transaction also confirms Addleshaw’s position as one of the leading players in the building society market, with the firm acting for almost half of country’s building societies and on every one of the last 15 merger deals.