Top of Group C owing to their nervy 1-0 success over Serbia on Monday night, the England will be assured of a top-two finish should they get the better of Denmark, who could only draw 1-1 with Slovenia in their opening tie.
Southgate's men have recent when it comes to defeating the Scandinavian outfit at the European Championships, having edged out Kasper Hjulmand's side in the Euro 2020 semi-finals, although their display against Serbia left something to be desired.
Nevertheless, England emerged triumphant and can now seal their place in the knockouts by triumphing at Deutsche Bank Park in Frankfurt, where almost all of Southgate's squad should be available for selection.
However, there was no Luke Shaw in team training on Wednesday morning, as the Three Lions announced that the Manchester United man is still undertaking his individual recovery programme.
Shaw has now gone four months without kicking a ball in a competitive match due to a serious muscular problem, which appeared to jeopardise his chances of a Euro 2024 call-up before Southgate opted to take a risk.
Shaw had begun to work with the team again before the victory over Serbia, which he was never expected to play in anyway, and there was hope that he would earn some valuable minutes against Denmark.
However, the left-back's availability has been plunged into slight doubt owing to his absence from team training on Wednesday, although it is not believed to be indicative of a fresh injury setback.
Instead, Shaw is simply believed to have been wrapped in cotton wool before Thursday's trip to Frankfurt, and there is still a chance that he could make his comeback as a substitute on Thursday.
Will Southgate make any England changes against Denmark?
With Shaw still working his way back to full fitness, another start on the left-hand side awaits Newcastle United's Kieran Trippier, who will likely form part of an untouched England XI for the second game running.
Reports had claimed that Southgate was considering swapping Phil Foden for Anthony Gordon after the Manchester City man's ineffective display against Serbia, but the England boss is set to keep faith with the 24-year-old.
Rumours that Cole Palmer could displace Trent Alexander-Arnold - thereby dropping Jude Bellingham into a deeper midfield role - are also thought to be wide of the mark, although Southgate could make some alterations against Slovenia on June 25 if England's knockout spot is sealed this week.