* C$ softens slightly against the greenback * U.S. private sector job creation lower than expected in May * Prospect of Fed slowing stimulus tied to labor market By Alastair Sharp TORONTO, June 5 (Reuters) - The Canadian dollar was little changed on Wednesday versus the U.S. dollar as weaker-than-expected U.S. private sector hiring restrained the greenback's strength, as it is seen reducing the prospect of the Federal Reserve changing its monetary stimulus stance any time soon. The moderate pace of hiring seen in May's U.S. ADP report of 135,000 new private sector jobs may not be enough to persuade the Fed to soon pare back its monthly purchases of $85 billion dollars of bonds. The Fed's bond buying aims to keep U.S. interest rates low, thus making the dollar less alluring for investors seeking higher returns on deposits elsewhere. The Canadian currency weakened considerably last month as robust U.S. economic data bolstered the view that the Fed would rein in its bond buying in the coming months. At 9:53 a.m. (1353 GMT) the Canadian dollar was trading at C$1.0353 to the greenback, or 96.59 U.S. cents, nearly 0.1 percent lower, as compared with C$1.0344, or 96.67 U.S. cents, at Tuesday's North American close. "Markets are all about U.S. dollar direction at the moment. Even dollar/yen is more dollar than it is yen," said Adam Cole, global head of currency strategy at Royal Bank of Canada. "When that's the case, the Canadian dollar tends to be relatively stable." Jobs reports for both the United States and Canada are due on Friday, with the U.S. print more closely watched given the Fed has explicitly linked policy direction to the health of the jobs market. After in recent months acting as a safe haven amid global economic uncertainty, the greenback is now strengthening in relation to stronger data and falling back on weaker numbers. "Now that you've got some movement in expectation of Fed policy expectations, it's more like a conventional world where good news is good news rather than good news is bad news," RBC's Cole said. A series of Reuters polls released on Wednesday showed that the greenback is seen extending its gains against a string of major currencies including the euro, pound sterling and yen, while the Canadian dollar is expected to hold steady. Canadian government debt prices were higher across the curve, with the two-year bond up 2 Canadian cents to yield 1.056 percent, while the benchmark 10-year bond rose 19 Canadian cents to yield 2.063 percent.