Chrysler CEO Sergio Marchionne with UAW President Bob King.

Fiat will purchase the U.S. Treasury’s remaining 6.6% stake in Chrysler for $560 million, and will now have the option to purchase the shares held by the United Autoworkers Union.

With the Italians set to acquire yet another 5% as it meets the third hurdle set by the 2009 federal bailout of Chrysler, and CEO Sergio Marchionne now hoping to buy the small stake held by the Canadian government, Fiat could wind up with 76% or more of the stock in Chrysler.

That has many analysts wondering whether Chrysler will skip the long-discussed return to public trading despite comments made by CEO Marchionne , last month, following the payoff of the U.S. maker’s bailout loans.

The sale of the American Treasury’s 98,461 shares in Chrysler placed an $8 billion valuation on a carmaker that emerged from bankruptcy almost exactly two years ago.

(Pres. Obama will visit a Jeep plant in Toledo today. Click Here for that story.)

The government’s sale of its 6.6% remaining stake followed Fiat’s purchase, last month, of a 16% stake for $1.6 billion.  That sale was triggered by the payoff of $5.8 billion in U.S. government loans and an additional $1.7 billion lent by the Canadian and Ontario governments too help Chrysler emerge from Chapter 11 protection.

After the bankruptcy, Fiat gained a 20% stake in the U.S. maker, but has so far added two 5% tranches for expanding Chrysler’s overseas sales and for introducing a new, high-mileage engine to the company’s line-up of powertrains.  A third 5% tranche will be awarded to Fiat once Chrysler launches a new model, expected by year-end, that gets at least 40 mpg.

The complicated process of building up Fiat’s stake now shifts to the UAW.  The union’s health car trust, known as a VEBA, currently holds 40% of Chrysler.  But Fiat has the right to acquire some or all of that stake between July 2012 and June 2016 – and it has indicated it likely will acquire at least some of the UAW holdings.

Fiat has already effectively merged management operations of the two companies and will consolidate their finances moving forward, a joint earnings report expected for subsequent quarters.

Until recently, CEO Marchionne was indicating plans to stage an IPO to return Chrysler to the stock market.  That appeared to be on target for late 2011 or possibly early 2012.  But there are growing indications that as the companies continue to meld Marchionne may no longer see the need, despite the potential billions it could pump into their treasuries.

“We believe that the step above 50%(in Fiat’s stake in Chrysler) now makes an IPO an even more unlikely scenario at this stage,” said Deutsche Bank analyst Rod Lache.

Following the news conference marking the payoff of the government loans, TheDetroitBureau.com asked the Fiat/Chrysler CEO whether it still planned to move ahead on the Initial Public Offering.  Marchionne replied that he wanted a way to “monetize” the outstanding shares in Chrysler, but he notably avoided mentioning either an IPO or a public offering.

He will have to make a firm decision in the months ahead.