The New York Stock Exchange (NYSE) has unveiled plans to merge with the pan-European Euronext exchange.
Euronext shareholders will meet on Tuesday to discuss the firm's fate
The proposed move would create a transatlantic stock market giant worth $21bn (16bn euros; £11bn).
If successful, the merger bid would trump rival plans by Germany's Deutsche Boerse for a tie-up with Euronext.
Euronext's board discussed the NYSE offer all Monday afternoon, and later said the proposal was "the most attractive combination".
It also said it would explain both proposals to its shareholders at the annual general meeting on Tuesday and make a final recommendation at a future extraordinary meeting.
Competition between exchanges has been increasing, and analysts are predicting more mergers as the companies look to cut costs and boost client numbers.
Earlier this year, Euronext called off its attempts to buy the London Stock Exchange after US firm Nasdaq increased its stake. Since then, Nasdaq has continued to build its holding, and said on Friday it now had now topped 25%.
With that deal off the table, the tie up with the NYSE becomes more important for Euronext, analysts said.
Euronext controls the Paris, Brussels, Lisbon and Amsterdam exchanges, as well as the London-based Liffe international derivatives exchange.
The NYSE has offered $10.2bn in cash and shares for Euronext, more than has been tabled by rival Deutsche Boerse.
Under the terms of Monday's deal, each NYSE share would be converted into one share of common stock in the merged company, which would be renamed NYSE Euronext.
News of the NYSE offer comes a day before Euronext's annual general meeting in Amsterdam, where shareholders are expected to consider the future of the company.
A merger between the NYSE and Euronext would see NYSE Group boss John Thain become chief executive of the combined group, with Euronext chief executive Jean-Francois Theodore becoming deputy chief executive officer.
"NYSE Euronext will be the world's most liquid and truly global financial marketplace, offering unparalleled benefits for investors and issuers in the United States, Europe and across the globe," Mr Thain said.
The NYSE was previously reported to be interested in making a bid for the LSE, which has so far rebuffed takeover approaches from Deutsche Boerse, Australia's Macquarie Bank and Nasdaq.
Separately, the Financial Times Deutschland reported on Monday that Deutsche Boerse was considering making an all-share offer for Euronext.
The German operator reaffirmed its interest in merging with Euronext on Friday.