* Dollar set for more gains on Fed outlook, economy * Sterling hits four-month low vs dollar after weak UK data * Euro flat; any bounce seen likely to fizzle out By Anirban Nag LONDON, July 9 (Reuters) - The dollar rose towards recent three-year highs against a basket of currencies on Tuesday, with more investors betting on further gains as the Federal Reserve prepares to reduce stimulus. The dollar's biggest gains were against the British pound, after weaker-than-expected UK data drove sterling close to a three-year low and highlighted the divergence between UK and U.S. monetary policy. Expectations the Fed, which releases minutes of its June meeting on Wednesday, will scale back its $85 billion-a-month in asset purchases as early as September are encouraging investors to buy dollars. The dollar index, which measures the greenback against a currency basket, was up 0.2 percent at 84.343, having earlier hit 84.085 on a dip in U.S. Treasury yields. It hit a three-year peak of 84.588 on Monday after an upbeat U.S. jobs report on Friday The euro was flat at $1.2860, holding above Friday's seven-week trough of $1.2806. The single currency, which began July above $1.30, found some support after Greece secured aid that will prevent it from defaulting in August. But with the European Central Bank set to keep rates at record lows, the euro is likely to remain under pressure. "This is momentum-driven trade and we are looking for more dollar strength," said Mankash Jain, head of FX and Investment Management at Solo Capital, London. "Any bounce in the euro towards $1.2950 is a time to initiate fresh short positions." Likewise, any modest decline in the dollar in coming days "will provide a renewed buying opportunity as the overall picture is positive for the dollar," said Ian Stannard, head of European FX strategy at Morgan Stanley. He said Wednesday's FOMC minutes would be scrutinised for any hints to when monetary stimulus could be reduced. STERLING DROPS Sterling hit four-month lows against the dollar and the euro after weak factory output and trade data was seen as raising the risk of the Bank of England easing monetary policy in coming months. Sterling fell 0.8 percent to $1.4832, its lowest since mid-March. A drop below $1.4832 would take it to a three-year low. "Short sterling/dollar remains a favoured trade and our view has long been that US-UK growth differentials are a convincing rationale for further downside," Commerzbank said in a note. The dollar was up 0.3 percent against the yen as the Bank of Japan is expected to maintain aggressive monetary stimulus when it meets to decide on policy later this week. The dollar rose 0.2 percent to 101.17 yen, off a near six-week high of 101.54 yen hit on trading platform EBS on Monday.