Southgate has been criticised for his rigidity through four uninspiring games but reports surfaced this week that he planned to switch from four at the back to three, which would allow him to employ his wing-backs higher up the pitch.
"We're always considering the best way to approach a game," he said. "We're always trying to prepare to give our opponents the best possible game."
Goalkeeper Jordan Pickford similarly sidestepped the question, saying there was not much difference between the two formations.
"It is about being balanced whatever formation you play," he said. "If it is a back three or back four, the shape won't change as much."
While Southgate would not confirm whether Luke Shaw will be in the team, the left back is finally fit to start having not played since February due to injury.
The manager also praised the "brilliant job" right-footed Kieran Trippier has done in that position.
"(Trippier) doesn't give that balance a natural left-footer would but his leadership, communication and his talking is phenomenal and it helps the wingers in front of them play their game," Southgate said.
England Progress
While England have yet to look anything like their pre-tournament billing as tournament favourites, Southgate said he has seen progress in training.
"You obviously want to play well as a team, your ambition is to play as well as you possibly can. Every team wants to excite, every team wants to score goals," said Southgate, who will manage his 100th game for England on Saturday.
"(But) we've played opponents who have made it very, very difficult for us," he added, after uninspiring games against Serbia, Denmark, Slovenia and Slovakia.
"And there's been a lot of expectation on the team in the early part of the tournament especially, so I feel that the team even in training now look in a different place mentally. They look more fluid, and I'm expecting us to play well."
Southgate bristled when asked if he had spoken to the players about taking their opportunity with the team being on the easier side of the draw. The manager was having none of it.
"That's a classic example of the entitlement we have as a nation, which creates drama and infuriates our opponents," Southgate said.
"We're playing a really strong football nation (Switzerland) who have played exceptionally well, well-prepared, have enormous pride. Our focus is on how do we win this game? How do we play it to the best of our ability?
"We've never been to a final outside England, we've only had two finals in our history, three semi-finals, so lots of nations who we might perceive as English people to be smaller have had far better records than us in terms of getting to the latter stages of finals (tournaments). It's half the problem we have.
"We definitely have huge respect for our opponents. And we know we've got to be at our very best to be able to win the game."
The winners will meet either the Netherlands or Turkey in the semi-finals.
