The proposed move with Lawrence Graham would create a firm with revenues of about £170m and more than 600 lawyers – almost 200 of which would be partners.
Wragge & Co senior partner Quentin Poole said: "We have been open about our strategy and the fact that we are looking at opportunities to strengthen our ability to serve clients in strategic practice areas, sectors or locations, particularly in London.
"Lawrence Graham has an excellent reputation, particularly for real estate, equity capital markets, investment funds and private capital, and a strong, collegiate culture. We are exploring how clients might benefit from our two firms forming closer ties."
Wragge & Co recorded a turnover of £120.5m in 2012/13 while Lawrence Graham reported almost £52m.
Lawrence Graham was founded in London more than 280 years ago and now has offices around the world in Dubai, Monaco, Moscow and Singapore.