* Euro rises to $1.3014 vs dollar * Hopes rise before euro zone finmin meeting on Greece * Dollar dented ahead of FOMC meeting * Australian dollar hits near 12-week high vs U.S. dollar By Jessica Mortimer LONDON, Jan 23 (Reuters) - The euro hit its highest level in nearly three weeks against the dollar on Monday on tentative optimism that Greece will cut a deal with its creditors on a debt swap, prompting a squeeze in short positions. Market players were looking to a euro zone finance ministers' meeting on Monday for a decision on the terms of a Greek debt restructuring ministers would be ready to accept in order to pave the way for Athens to access a second bailout package and avoid a chaotic default. However, the single currency was still vulnerable to renewed weakness as uncertainties remained about the outlook for Greece and other highly indebted euro zone countries. Private creditors said on Sunday they had come to the limits of what losses they could concede, putting the ball in the court of the European Union and the IMF. The euro was supported by investors taking profit on short positions. Data showed speculators boosted net euro short positions to a fourth straight record in the week to Jan. 17. "IMM data shows short positions are extremely stretched and we're seeing a squeeze today," said Lee Hardman, currency strategist at BTM-UFJ. The euro was up 0.4 percent at $1.3001 after hitting its strongest since early January at $1.3014 on EBS. Traders cited demand from Middle East accounts that lifted the currency and helped to trigger stop-losses on the break of Friday's high of $1.2986. "The likelihood is that the (Greek debt) talks will converge somewhere where a deal is still voluntary," said Ankita Dudani, currency strategist at RBS. Resolving the issue of a Greek debt swap is key to putting Athens' debt on a sustainable path and avoiding a chaotic default that could threaten the whole currency bloc. Markets had hoped for an agreement over the weekend, and analysts said they were still betting on a deal, leaving room for disappointment. "It is uncertain what will happen with the restructuring of Greek debt, and after that there will be tough negotiations with the EU and the IMF about the next financing facility," said Niels Christensen, currency strategist at Nordea in Copenhagen. The technical outlook for the euro was improved by last week's break above the 21-day moving average at $1.2870 for the first time this year. The common currency slumped to a 17-month low of $1.2624 earlier this month. Traders said a break back below $1.2870-80 could see major support at $1.2800-10 tested. DOLLAR DIPS For the wider market, the Federal Reserve's two-day policy meeting starting on Tuesday will be the major event. Although no policy change is expected, the Fed could take the historic step of announcing an explicit target for inflation as part of its new communication strategy. Traders said wariness ahead of this meeting and expectations of a continued easy monetary policy was helping to weigh on the dollar, pushing the dollar index below the 80.0 level. It was last down 0.4 percent on the day at 79.879. The Australian dollar hit a near 12-week high versus the U.S. dollar at $1.0563, with investors favouring the high-yielding currency and the sound fundamentals of the Australian economy. The euro was up 0.4 percent against the yen at 99.93 yen , taking it close to last week's peak at around 100.33.