The man who wanted to buy the London Stock Exchange?
The very same. He got rebuffed good and proper when he came calling over here in 2006, but he is no less hungry for Nasdaq to do deals. Perhaps more so.
These days he is after a rather different icon of capitalism, but this time it is a little closer to home: the New York Stock Exchange.
Can't a man just be happy with what he has?
Not likely. When it comes to running a big exchange, bigger is better business. There are savings to be had from combining all the computers and cutting staff, and traders appreciate the greater liquidity of larger exchanges.
And conquering an old rival can't feel too bad either, eh?
So far Mr Greifeld looks less like a conquering hero than a pesky irritant. NYSE Euronext has told him to take his $11.2bn bid and shove it. It has already vowed to merge with Europe's Deutsche Börse.
How's he taking it?
Well, Mr Greifeld's motto is: "You never get what you want the first time you try." And he is a man with stamina, having completed marathons all over the world and gone running every morning for years.
He has shown determination all his life. He grew up in Queens, New York, the son of a postman, and got a scholarship to college. He got the top job at Nasdaq in 2003 after a career at technology companies, but if he doesn't consummate this deal, it could be curtains.
The fact that Nasdaq is really stretching itself to make its bid – even teaming up with the ICE commodities exchange – shows how desperate the situation is. As consolidation speeds up in this industry, it is a case of eat or be eaten. If Deutsche Börse walks off with NYSE, it could be the end of Mr Greifeld's acquisition attempts – for good.