* Acquisition of Irish Stock Exchange helps Q2 core earnings
* PE firms want to offload stakes in trading firms- CEO
* In "normal dialogue" with UK regulators over Brexit-CEO
* GRAPHIC: tmsnrt.rs/2O9HxyB (Adds interview with CEO)
By Noor Zainab Hussain and Huw Jones
LONDON, Aug 3 (Reuters) - Euronext is interested in making further acquisitions to move its business away from pure share trading, the exchange's chief executive Stephane Boujnah said on Friday, as long as the price is right.
The pan-European bourse runs markets in Paris, Amsterdam, Brussels, Dublin and Portugal.
But it is heavily dependent on share trading for revenues and is already taking steps to diversify by moving into foreign exchange and buying the Irish Stock Exchange, which lists bonds.
Boujnah said more needs to be done to "diversify the topline", though he was having to compete with richer rivals.
"We want to do smart deals rather than expensive, stupid deals," Boujnah told Reuters after Euronext released second quarter earnings.
"We pass on opportunities because they don't meet our financial discipline threshold. They are far too expensive, or we compete with much deeper pocketed bidders who are willing to pay multiples that are well beyond our self-imposed acquisition discipline."
Some private equity companies are looking to offload stakes in trading firms, which Euronext may be interested in, Boujnah said without giving further details.
Euronext's big U.S. rivals have been snapping up trading operations, with ICE completing its acquisition of the Chicago Stock Exchange last month and CME announcing plans to take over NEX Group in March.
"There will be opportunities. All the big private equity guys were acquiring some of these assets, are in the process of considering reselling them. It's clearly a very busy space in the industry."
Second-quarter core earnings rose 11.9 percent to 88.6 million euros ($102.7 million), helped by its acquisition of the Irish Stock Exchange, higher listings and a rise in trading volumes.
The departure of Britain, Europe's biggest capital market, from the European Union next March is forcing exchanges to implement contingency plans in case of disruption to cross-border trading links.
Turquoise, the pan-European share trading platform owned by rival London Stock Exchange Group is applying for licence in Amsterdam, as is London-based Cboe Europe. Deutsche Boerse is trying to lure clearing of euro-denominated transactions from London.
Boujnah said Euronext was having "normal dialogue" with regulators about continuity of flows between customers in London and the exchange.
"We don't foresee any major problem for the moment on this front for core business," Boujnah said. Euronext is already fully regulated by Britain's Financial Conduct Authority.
Euronext said cash trading revenue rose 7.1 percent to 53.9 million euros in the quarter, in an environment of "persisting low volatility".
Volatility is an important driver of trading across a range of asset classes, including futures, exchange-traded funds and cash equities.
Reined-in costs and rising volumes helped Euronext to cope with relatively calm markets last year, compared with 2016 when the U.S. presidential election and Britain's vote to leave the European Union boosted volatility.
The trade war between the United States and China, however, has sparked market volatility in recent months.
($1 = 0.8627 euros)
Reporting by Noor Zainab Hussain in Bengaluru; Editing by Gopakumar Warrier, Bernard Orr and Jan Harvey