Al Jazeera's Tony Cheng, reporting from the capital Beijing, said that by "eligible", authorities mean young, urban couples who are relatively well off.
|Shanghai says the move is to shield against an ageing population [EPA]
Friday's announcement did not amount to a reversal of the country's longstanding "one-child" policy, but the government appeared to be experimenting as it re-examined the policy across the country, our correspondent said.
China's "one-child" policy is actually far less rigorous than its name suggests, with many exemptions, he added.
For example, urban parents can have two children if they themselves are both only children, or they pay a relatively small fine to have a second child. And rural couples are allowed a second if their first is a girl.
Still, since the late 1970s, the government has always pushed to keep families as small as possible, worried about population growth outstripping limited resources.
But Shanghai is now apparently focusing on a new, growing concern: the burden of an ageing population on the generation born since the "one-child" policy was started.
More than one-fifth of Shanghai's residents or three million people, are already above 60-years-old, and that proportion is expected to rise to around one-third by 2020, the China Daily said.
China is ill-prepared to cope with its greying population, with an under-funded state pension system and shrinking family sizes removing a traditional layer of social support for elders.
The US-based Centre for Strategic and International Studies warned in April that by 2050 China will have more than 438 million people older than 60, with more than 100 million of them aged 80 and above.
That means the country will have just 1.6 working-age adults to support every person over 60, a far cry from the 7.7 to one ratio in 1975.