Southgate took a gamble on Shaw's fitness and named the full-back in his 26-man squad for Germany, despite the Manchester United star missing the second half of the season with a muscle injury.
It had been hoped that Shaw could return to full fitness in time for England's knockout games and while the 28-year-old has been pictured in training with the rest of the squad, he is not deemed ready for a starting role in Dusseldorf.
Kieran Trippier has filled in at left-back in Shaw's absence and the Three Lions have been noticeably lacking in pace and creativity down that flank, with Southgate's men facing heavy criticism for their underwhelming performances at the tournament.
But with Marc Guehi forced to sit out the quarter-final through suspension, Southgate is expected to switch up his formation and field a back-three versus Switzerland, which will see Arsenal's Saka start at left wing-back - something Wright had previously raised as a potential solution.
'It would be a shame,' the legendary ex-Arsenal striker said on the latest episode of The Overlap.
'I mentioned it previously because our manager... it's so thick not too bring a back-up to Luke Shaw and it [Saka at left wing-back] was something that I mentioned as a solution.'
'I'm not bothered about what they're saying! The fact is that I put a question to everybody about now we haven't got a left-back, we've got someone who has played there, so you ask the question,' he added.
'People can do that [criticise], I'm not bothered about that. I'm more talking about getting that left side going.
'So if it's Luke Shaw and he can do it then that's fine. If Gareth now says he's going to play Saka there then hopefully that will get in going.'
'He'll be okay! In the end, he ended up at right wing-back as well at one stage,' Wright continued.
'But what I am more concerned about is the fact that our manager didn't bring a back-up which is just crazy and so that's why that might have to happen.
'I'm just pleased that something might change because something has to change.
'We've got to where we are and I'm really happy about it, I'm not going to be down on the guys. We've shown that we've got players that can pull it out the fire.'
Ian Wright blasts UEFA rule after Spain beat Germany in dramatic Euro 2024 clash
'You know something? I was going to say 3-2 to us because I think they will score a couple,' he predicted.
'I believe Phil [Foden] and Saka and [Jude] Bellingham... I believe that this is the time and this is where we can cause them problems.
'I think it's going to be harum-scarem. I'll go 2-1 because that'll be just as exciting.'
For more stories like this, check our sport page.
Follow Metro Sport for the latest news on Facebook, Twitter and Instagram.
MORE : England vs Switzerland: Build-up to Euro 2024 quarter-final clash
MORE : William Saliba reacts to shutting out Cristiano Ronaldo in France's Euro 2024 win over Portugal
MORE : Arsenal legend Jens Lehmann slams Germany star over his pink hair and asks if he 'feels like a woman'
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.