The UK and US are preparing to give the nod in private - with a change in position confirmed only after the first missiles have been fired, Report informs via LBC.
Diplomatic sources said the US is keen to see a plan first from President Zelenskyy on how it could help see them through the winter months of the war.
A final decision could be rubber-stamped as soon as the UN General Assembly next week.
The UK and France have already sent the storm shadow missiles to Ukraine, but only for use on targets within their own borders
President Zelenskyy has been pushing for permission for months to use the missiles to strike deep inside Russia in a bid to target ammunition factories and other points.