It is thought China may pay about 70bn euros ($100bn) into the fund, which is expected to be boosted to 1tn euros.
Meanwhile French President Nicolas Sarkozy said debt-ridden Greece's entry to the eurozone was a mistake.
Greece was "not ready" when it joined in 2001, he said, adding that it could be rescued thanks to a new deal on the debt crisis.
European leaders worked into the early hours of Thursday in Brussels to secure an agreement aimed at preventing the crisis from spreading to larger eurozone economies.
The deal triggered a worldwide shares rally.
'Regular buyer' Beijing has made it clear that it will demand strong guarantees on the safety of any contribution it might make.
AnalysisWhile the head of the fund, Klaus Regling, described this as a regular meeting, it is being seen as the start of a process which could yield an agreement.
With vast reserves, Beijing is certainly in a position to invest but like any other investor China will want to make sure its money is safe.
In the past, overseas investments made by China's sovereign funds have soured leading to criticism back home.
"I cannot say today, and it's certainly far too early to say what kind of amounts might be envisaged."
He said China had been a regular buyer of EFSF bonds in the past.
He would present the fund's bonds as a potential commercial investment to China, he said, adding that Beijing regularly needed to find safe investments for its trade surpluses.
Chinese Vice Finance Minister Zhu Guangyao said there was work still to be done.
"We need to wait for the technicalities to be clear and also to carry out serious studies before we can decide on investment," he said, quoted by AFP.
"We hope that all these technical and specialised arrangements can be thrashed out at an early date and can be implemented and feasible. That will be very important for the effectiveness" of the fund.
The President of the World Bank, Robert Zoellick, has said he believes China will invest in Europe only if there are incentives for it to do so.
"I don't think that China will just come in as a white knight to try to provide money just to bail out Europeans," he told the BBC.
But investor Jim Rogers said China was prepared to help.
"From China's point of view, it's cheap foreign aid. They'll buy goodwill. I guess they'll put up some money," he said on BBC Radio 4's Today programme.
The main provisions of Thursday's deal are:
- German economist, aged 61
- 1975-2001: Worked at various times for IMF, German Finance Ministry and in private sector
- 2001-08: Director General of the European Commission's Economic and Financial Affairs directorate
- July 2010: Head of EFSF
- Banks holding Greek debt are to accept a 50% loss
- A new mechanism is to boost the EFSF
- Banks must also raise more capital to guard against losses resulting from any future government defaults
Asian markets rose for a second day on Friday and bank stocks in Europe continued to rally, a day after the deal was reached.