Asda or Morrisons will go unless they can perform a mega transformation.
You can't have Aldi and Lidl growing so much without a casualty elsewhere. In retail, it's all about displacement. The pool of shoppers and their spending power doesn't change much, so when new entrants come in, something/someone had to give.
Aldi and Lidl have captured the bottom end. Places like Iceland, B&M, HomeBargains have captured the "sell off" end of the brands.
Sainsbury and Tesco are going great guns for the upper middle end of the market. Booths, M&S and Waitrose have the top end.
That leaves Asda and Morrisons in limbo, as they used to be the cheaper end of the market.
They either need to adapt to compete with Lidl and Aldi or they need to improve their image/product range to compete with Sainsbury and then M&S/Waitrose, etc.
At the moment, both Asda and Morrisons don't seem to have a target market anymore, they don't know what they stand for. Morrisons especially lost out big time being slow to home deliveries, and they used to stand out with their fresh meat, fresh fish, bakery, etc., (i.e. their "marketplace") which they seem to be scrapping.
I'd put my money on it being Morrisons who go under. I think Asda have strong enough US backing to be able to perform a miracle U turn.