In his New Year message, the Labour leader said he was committed to "tackling issues around childcare, which lots of working parents face."
Lucy Powell, the Shadow Minister for Childcare, said: "I'd love it to be (introduced)," although she accepted its high cost meant it could take a decade or more to implement in full.
"My job is to make the political and economic case for childcare. If you invest in childcare, it pays for itself over time because it increases maternal employment rates," she added.
Labour is already committed to using a bank levy to provide 25 hours of free childcare a week for working parents with three and four-year-olds, worth £1500 a year.
Last month, the SNP Government's White Paper promised parents in an independent Scotland a massive increase in free childcare; the annual cost has been estimated at £1.2 billion.
Yet, its opponents have accused Alex Salmond and his colleagues of cynicism, insisting childcare policy is already devolved to Holyrood, meaning changes could be implemented now.
Nationalists said Holyrood cannot act sooner because the economic dividends of employing more women would not flow back to Edinburgh but directly to Whitehall, but independence would change this.