The first minister said hairdressers could be among the shops to reopen as early as 15 March, but warned any easing would be gradual.
“I don’t believe it will be a wholesale reopening, we are going to do things in the way that Sage and the WHO recommend – carefully, step-by-step, always assessing the impact of any actions that we take,” he told BBC Breakfast.
He added: “I will set out today some discussions that we will have with non-essential retail over the next couple of weeks to see how we might begin the reopening of non-essential retail.
“If it is possible from 15 March to begin the reopening of some aspects of non-essential retail and personal services such as hairdressing then of course that is what we would want to do.
“But it will be, as I say, in that careful step-by-step way and always making sure that we are carefully monitoring the impact of any lifting of restrictions on the circulation of the virus.”
He said the devolved government would also work with tourist companies to look at easing of rules around Easter.
Additionally, all primary school children in Wales will return to face-to-face teaching from mid-March provided the coronavirus situation in the country “continues to improve”, with Covid-19 cases at their lowest level since September. Mr Drakeford said.
Wales, like the rest of the UK, is currently under a stay-at-home order.
It comes as Boris Johnson faces a tug of war between scientists and some Conservative MPs over when and how to roll back lockdown rules in England.
The PM has pledged his roadmap, to be unveiled on 22 February, will be “cautious but irreversible”.