The Church of England press office has refused to confirm the appointment of Welby, the current Bishop of Durham, but Ladbrokes and William Hill suspended betting on the next Archbishop after a flurry of bets on Bishop Welby.
Asked what qualities the next Archbishop of Canterbury would need to have, Dr Williams quoted from the great theologian Karl Barth.
"I think it was put very well by a theologian of the last century who said, 'You have to preach with a Bible in one hand and a newspaper in the other'," he said.
"You have to be cross-referencing all the time and saying 'How does the vision of humanity and community that's put before us in the Bible map onto these issues of poverty, privation, violence and conflict?'
"And you have to use what you read in the newspaper to prompt and direct the questions that you put to the Bible: 'Where is this going to help me?'
"So I think somebody who likes reading the Bible and likes reading newspapers would be a good start!"
The Crown Nominations Commission met no less than four times to consider the next Archbishop of Canterbury.
Other leaders considered for the role were the Archbishop of York, Dr John Sentamu, and the Bishop of London, Dr Richard Chartres.
Bishop Welby is an Old Etonian and has a business background in the oil industry.
He has been Bishop of Durham little over a year and opposes gay marriage but supports women bishops.