It depends. If you have absolutely no luxuries and are living between each pay check with nothing spare or adding to debt each month, plus can not possibly move to a cheaper rental, then no.
But if you rent (assuming private rental), surely you must have access to some small savings already as you could be given notice at any time and would have to pay deposit on a new rental before getting your deposit back.
I know of plenty of people who say they can't possibly afford to save anything towards a house deposit but still have Amazon Prime/ Netflix subscriptions, are often posting orders in cosmetics Facebook groups, go on semi-expensive holidays each year, eat out and have takeaways, have expensive mobile bills monthly (I have a £5 a month contract and bought a second hand phone, I can't understand people paying £50+ per month), could cut down their alcohol bills each month, cut some off their weekly shopping if they don't buy expensive brands, have their heating on and wear a t-shirt in winter, constantly buy bits of furnishings for their house, buy new clothes.
Now I'm not judging anyone for any of that, if they want Netflix and a takeaway every week to enjoy life, then that's great - but it's not true that they can't save anything, just that they don't want to change their lifestyle in order to do so.
On top of that there's looking at shared ownership, moving to a cheaper area, buying a cheap small house/ flat to rent out to get you on the property ladder while you still rent.
I just think it's quite easy for many to say they can't possibly, when a good percentage of them actual could if they wanted to.