The Tory leader made the offer in a speech in Edinburgh, where he set out his defence of more than 300 years of political union between Scotland and England.
“This doesn’t have to be the end of the road,” he said.
“When the referendum on independence is over, I am open to looking at how the devolved settlement can be improved further.
“And, yes, that does mean considering what further powers could be devolved.
“But that must be a question for after the referendum, when Scotland has made its choice about the fundamental question of independence or for the United Kingdom.