Euronext, the owner of the Irish Stock Exchange since 2018, is pitted against Switzerland's Six and Frankfurt's Deutsche Boerse in a dog-fight to be the consolidator in Europe's fragmented stock markets ahead of the EU's proposed 'capital markets union'.
Euronext already operates stock exchanges in Dublin, Paris, Amsterdam, Brussels, Oslo and Lisbon.
Adding Borsa Italiana - the big and busy Milan stock exchange - would represent a major step towards Euronext's goal of positioning itself as the backbone of the EU's planned capital markets union and rival the major money centres in Frankfurt and London.
That could be good news for Euronext Dublin as an English language access point to what could become a post-Brexit European financial giant.
"At the top level this is all about leveraging technology and consolidating data across geographies," said a market source who advises publicly listed companies. "With so much uncertainty around Brexit, there may be an opportunity in an English-speaking exchange for companies seeking a European listing."
Euronext bought the Irish Stock Exchange in 2018 for €137m. The deal produced major cash windfalls for its local stockbroker owners but has diluted both the Dublin market's own identity and its historic ties to London, the regional giant.
The ISE chief executive who executed the transaction, Deirdre Somers, said at the time that the sale was "a pivot toward the EU... it's the ISE saying our future is in Europe".
Euronext's bid for the Milan exchange is its pivot towards scale. The combination of markets from Dublin and Lisbon to Oslo with Paris, Amsterdam and Milan - with Milan the biggest part of an enlarged group - would make it the EU's most important markets operator at a time when the Union aspires to consolidate capital markets so that businesses across the Union are better able to raise capital as quickly and cheaply as companies can in London or New York.
Euronext's ambitions also seem to chime with the preferences of the Italian government, whose market watchdog has a veto over any major ownership changes for the Milan bourse.
Amid bid speculation last week, Italian finance minister Roberto Gualtieri said that he hoped that Borsa Italiano "will find its strategic place within the euro zone's single market, with industrial and financial partners that can sustain and reinforce, in the best possible way, the project of a European capital markets union".
Euronext's local partners in the offer include Italy's Cassa Depositi e Prestiti and Intesa Sanpaolo, potentially firming up its case in Rome.
But it faces competition. Swiss stock exchange Six has emerged as its chief rival to buy Italy's Borsa Italiana and has ambitions of its own.
The Zurich-based exchange beat Euronext to acquire Spain's BME earlier this year.
Euronext and Deutsche Boerse confirmed last Friday that they were making offers for Borsa Italiana, which is being sold by the London Stock Exchange to clear regulatory hurdles in its own bid for data provider Refinitiv.
Deutsche Boerse's effort to merge with LSE was blocked in 2016 on competition grounds, and it knows the business well.