Southgate has persisted with a four-man backline of Stones, Kieran Trippier, Kyle Walker and Marc Guehi throughout the tournament so far, but the latter is banned for the quarter-final due to an accumulation of yellow cards.
England's defence has been one of the strong points of their underwhelming Euro 2024 campaign so far, but they have still come under the cosh quite often and were at sea for Ivan Schranz's opener for Slovakia in the last 16.
Southgate is expected to deploy Aston Villa's Ezri Konsa in Guehi's absence in the quarter-final, and the 53-year-old is said to be giving consideration to playing with three centre-backs to match Switzerland's setup.
Konsa and Stones would likely join Walker in front of Jordan Pickford in that case, although it is unclear whether the Three Lions would opt for a 3-4-3, 3-4-2-1, 3-5-2 or other variation of the system.
Stones backs England to "click" with three-man defence
Walker and Stones already possess plentiful experience of playing in a three-man wall with Harry Maguire - as was the case at the 2018 World Cup - and Stones was quizzed on how England could cope with the change in his pre-game press conference.
The Manchester City man recalled previous instances where the Three Lions have used a system of three centre-backs, and he expects his teammates to enjoy a "seamless" transition if England are to change their formation.
"We've done it in previous tournaments. I remember [beating] Germany [during] the last Euros. Previously to that in 2018," Stones told reporters, as quoted by The Guardian.
"I think it's a great thing to have in the locker if we need to play that system. It's something that shouldn't be underestimated for us as a team - that we can do it so easily and seamlessly, and kind of click together."
Stones has been seen with strapping on his knee in training this week, raising fears that the ex-Everton man could be carrying a quarter-final-threatening injury, but he allayed concerns that he could miss the clash with Switzerland.
What England selection dilemmas must Southgate solve?
News of Stones's fitness will no doubt come as a huge relief to Southgate, who is facing predicaments out wide, in midfield and up front for Saturday's quarter-final, which England enter having won just one of their Euro 2024 matches in 90 minutes.
There is still no indication that Luke Shaw will be fit to start - the Manchester United man has not earned any minutes at the competition so far - meaning that Bukayo Saka might have to be shoe-horned into a left-wing back role.
Trippier and Trent Alexander-Arnold could therefore battle for the right to start as England's right wing-back, while Jude Bellingham is thought to have escaped a ban for his crotch-grabbing celebration against Slovakia.
The Real Madrid man is arguably one of four midfielders competing for a maximum of three central spots - Declan Rice, Kobbie Mainoo and Phil Foden are the others - while Southgate must also decide whether to continue with Harry Kane as the lone striker or pair him up with Ivan Toney, who made a telling impact off the bench in the last 16.