Nasdaq may bid for the London Stock Exchange by October, according to Robert Greifeld, Nasdaq’s Chief Executive.

If Nasdaq succeeds in buying the LSE it would allow the American exchange to compete for listings with the new NYSE-Euronext and consolidate trading systems to cut costs.

A combined Nasdaq-LSE would allow companies to list their shares in both London and New York and offer traders on both sides of the Atlantic a way to buy and sell stocks through a single trading system. Sorting out the regulatory tangle may prove a tougher nut to crack than resolving the ownership issue, however.