* FTSEurofirst up 0.3 percent
* Fears over U.S. fiscal cliff ease
* Miners extend value rally
* Nokia rallying on Lumia sales hopes
By David Brett
LONDON, Dec 18 (Reuters) - European shares rose close to 2012 highs on Tuesday on signs that U.S. lawmakers might reach agreement to avoid looming tax hikes and spending cuts that threaten to hurt the world's biggest economy.
By 1132 GMT, the FTSEurofirst 300 was up 3.49 points, or 0.3 percent at 1,136.01, nearing its peak for the year of 1,141.32, as was France's CAC, at 3,638.87.
Shares gained after U.S. President Barack Obama made a counter-offer to Republicans that included a change in position on tax hikes for the wealthy, according to a source.
But with the CAC and FTSEurofirst near year-to-date highs and Germany's DAX at fresh 2012 highs, and with no formal U.S. deal on the table, investors were not getting carried away.
"It is a concern because it would not be great if the world's biggest economy fell back into recession," Andrea Williams, European fund manager at Royal London Asset Management, said.
"(But) I would like to think the parties would get themselves sorted and not let the economy go back into recession again but you have to have faith in the politicians," she said.
Shares in Nokia jumped 5 percent on expectations for good sales of its new Lumia smartphone models in the crucial Christmas shopping season, a trader said. Shares of the Finnish company have plunged 17.5 percent this year as the company, once the world's biggest mobile phone maker, has lost market share to Apple and Samsung.
Basic resources shares were the best-performing stocks by sector. Having underperformed broader markets by up to 25 percent this year, the sector has risen 10.8 percent in the last month on valuation grounds and reassuring economic data from China.
Elsewhere, security firm G4S rose 3 percent, shrugging off the recent negative sentiment surrounding its Olympics tender to trade better on a Financial Times report that a government contract relating to welfare reform is about to be awarded.
Flows into European equity funds climbed to a three-month high last week as U.S. investors beefed up their exposure to Europe, according to EFPR data.
The renewed demand for European shares has been driven by the data from China, a European Central Bank pledge made in September to do what it takes to save the euro, and optimism that a U.S. budget deal will be struck.
Williams at Royal London Asset Management is cautious about equities, saying the risk of further problems in Europe cannot be ruled out, but is "overweight" on telecoms and healthcare for dividend exposure.
Her big sector bet is insurance over banks, where she has been reducing her investments on concerns over further capital raising.
She is also "overweight" on industrials for their emerging market exposure.
Industrials were among the top performers on Tuesday with the sector index up 0.4 percent and winners included Swedish compressor and mining gear maker Atlas Copco, which was 0.8 percent higher.
Volumes suggested the seasonal wind down had already begun with indexes trading at around 35 percent of their already weak 90-day daily average, which sets the scene for some choppy sessions heading into the Christmas break.
"This could add to any intraday volatility but as has been the case since the Presidential election, it's going to be the fiscal cliff that stands to dominate market sentiment for now," Fawad Razaqzada, Market Strategist at GFT Markets, said.