The Three Lions are currently sitting top of Group C with four points to their name after beating Serbia and drawing against Denmark.
Southgate's troops have already secured their place in the last-16, with their progression assured following Spain's 1-0 victory over Albania.
However, they still have work to do to clinch top spot in Group C, as they look to avoid a potential last-16 tie against the likes of Germany and Portugal.
Southgate has had the majority of his squad available for the first two matches, but he has had to cope without the services of left-back Shaw.
Southgate confirms Shaw absence
The Manchester United defender has continued to work on his recovery from a hamstring injury he sustained in February.
Shaw has been working on an individual programme for most of his time in Germany, before he returned to team training on Monday to step up his rehabilitation process.
Although Shaw's presence was a welcome boost, Southgate has confirmed the 28-year-old remains unavailable for England's final group game against Slovenia.
"Luke's the only one that's not really available," Southgate told reporters at Monday's pre-match press conference. "He'll possibly change with the team tomorrow, but he's not quite ready to be involved in the game."
Trippier to continue in left-back role
Southgate opted to overlook the likes of Ben Chilwell and Tyrick Mitchell and a take risk by including Shaw as his only natural left-back option.
As it stands, the risk has not paid off because Southgate has been forced to use Kieran Trippier on the left side of defence, which has effectively taken the option away for England to have an overlapping left-back.
Trippier is expected to continue in the role despite recent reports suggesting that he is struggling with a calf issue.
While Trippier is set to retain his place, Liverpool's Trent Alexander-Arnold is likely to drop down to the bench for Tuesday's clash with Slovenia.
Southgate has been experimenting with Alexander-Arnold as a central midfielder, but it appears that the England boss will now turn to Chelsea's Conor Gallagher, who has featured as a substitute in the opening two matches.