By Jorn Madslien and Laurence Knight BBC News
Chinese yuan next to the US currency
China has plenty of money and would be able to help, though it is not a given that a cash injection will be beneficial for European nations
With some $3.2 trillion (£2tn) in its foreign reserves coffers, China may well be a natural contributor to the eurozone's bailout fund.
But the fact that China is a wealthy country, and therefore able to help, does not explain why China would actually want to do so.
One obvious reason might be a desire to prevent the crisis from leading to a recession in Europe - China's biggest export market.
Moreover, if the eurozone crisis were to spread globally - just as the US mortgage crisis did in 2008 - not only could it damage China's other trade partners, but also China itself.
Beijing recently had to intervene to shore up its own banks, which many investors fear are riddled with bad debts. Another global financial crisis could leave those banks in even worse shape.
Feeling the pinch
With consumers in Europe - and indeed in the US - already scaling back consumption and repaying personal debts, the demand for stuff made in China is slowing and could stay weak for years.
A worker monitors the loading of containers in Qingdao, China China's exporters would be hit if Europe was to suffer an economic recession
On the domestic front in indebted European countries, a reduction in imports is generally deemed beneficial, as it helps reduce their trade deficits. Or to put it another way, if consumers cut back, it is better for a country if they spend less on stuff made abroad and maintain spending on goods made at home.
But of course, China is not the only one that will take a hit as global consumption and trade slows to a trickle. Exporters - especially in trade surplus countries such as China, Japan or Germany, but also in trade deficit countries - will feel the pinch.
In turn, this general reduction in global trade will cement stubbornly high unemployment levels in the industrialised world, doing little to alleviate the crisis or to reduce the risks of it spreading beyond Europe.
But to the extent that the burden of shrinking demand falls on exporters like China, that means more of the job losses will be Chinese jobs.
Indeed, as global demand weakens, there is less point in keeping up massive investment in manufacturing in China. So perhaps it would be better to invest elsewhere?
China has long said it is eager to invest in Europe. But there are different ways for it to do so.
Banesto bank in Spain Europe's weakest economies may need investment, but China is not about to get involved
The one discussed in the context of the eurozone bailout fund would be an investment in European bonds, which equates to lending money to European governments.
This is not to say China is about to lend money directly to countries that need it the most.
Buying Spanish or Italian bonds may not be a tempting proposition, while buying German bonds clearly is, as they are deemed more likely to be repaid in full.
China has made it clear that it would only want to make sound investments, so it would require guarantees.
A Chinese contribution to the European European Financial Stability Facility (EFSF) would thus, in practice, differ little from a loan to Germany.
And that, of itself, would do little to help the likes of Spain and Italy manage their finances.
Indeed, Michael Pettis, international finance professor at Beijing University, says that Europe - or at least Germany - has plenty of capital of its own, and shouldn't even need China's money.
Prof Michael Pettis, finance professor at Peking University, says Europe "shouldn't turn to poor Asian countries"
He says that if China invests more capital in Europe, it may perversely end up putting more Europeans out of work.
By increasing its total investment in the eurozone, China is likely to push up the euro's value.
And that would make the eurozone's exports less competitive in international markets and Chinese exports more competitive in Europe - hardly an outcome that will help struggling Mediterranean countries.
Moreover, investing in government bonds is a very different proposition from investing in assets such as buildings, factories or infrastructure - the sort of investments that would deliver economic growth and create jobs.
Such investment is hard to come by these days, and transferring eurozone government debts from Europe's banks to China is not expected to do much to alleviate the situation.
As European governments repay their loans to the banks, the cash is likely to be absorbed by banks to help them with their recapitalisation. So it may not result in fresh funds being freed up for loans to companies.
In other words, Chinese investment in European bonds may do little to bolster economic growth in Europe.
Chinese investment directly into the real economy in Europe could well have a much greater effect.
Whether European voters would welcome Chinese buyers of real estate, companies and roads at a time when prices are depressed by the ongoing crisis is another matter.
But compared with the non-tangible rewards China is likely to demand in return for formal financial support - such as an early European Union recognition as a market economy, greater voting rights within the International Monetary Fund, a lifting of a ban on European arms sales to China, or silence around the matter of China's supposed efforts to keep its currency artificially weak - that may be a small price to pay.