The centre-back has been back in full training with his England team-mates this week to press his case to start.
Southgate has been encouraged by Maguire's speedy recovery and his response to treatment at St George's Park over the past two weeks, but is determined to take a cautious approach with one of his key players, in the hope he will be able to see out the rest of the tournament once he does return.
John Stones started alongside Tyrone Mings against Croatia on Sunday and Southgate is considering sticking with that partnership and giving Maguire a few days longer to work on his fitness.
Southgate is also giving Jack Grealish special treatment as he aims to make the Aston Villa playmaker one of the stars of the Euros.
Grealish was a surprise omission from England's opening game and underwent an individual programme at St George's yesterday.
The manager believes Grealish can be a pivotal figure as the tournament progresses, which is why he picked him in his squad, despite an injury-
disrupted end to his season. But he was always concerned about the 25-year-old's ability to withstand the rigours of so many games in such a short space of time after suffering a shin problem in February.
Grealish returned to action for the final games of the season, but England's medical staff are still monitoring his condition with a tailored approach to his training.
That Southgate kept him separate from the rest of the group yesterday is evidence of the ongoing caution he is taking with a player seen as being able to provide England with an 'X Factor'.
There was a growing feeling that Grealish would start against Croatia after impressing in the warm-up games against Austria and Romania. But Southgate played Raheem Sterling and Phil Foden alongside Harry Kane, and it paid off, with Sterling scoring the winner.
England's manager still believes Grealish can be influential up front or in a midfield role at this tournament and is preparing to introduce him in the upcoming games.
Meanwhile, Mings has said the squad are ignoring "background noise" about Kane's role in the team ahead of Friday's clash.
Kane was quiet against Croatia and former England player Jamie Carragher said this week that the Tottenham striker is no longer one of the untouchables in the England side.
But Mings has described questions around Kane as "irrelevant", because he is so important to England.
"He is one of the best players in the world and I think so highly of him," said the Aston Villa defender. "I played against him in the second to last game of the season. Let me tell you, he is not a player you can just let drop in, because when he turns and faces you up, he can pick out pretty much any pass he wants to.
"I can't speak highly enough of him as a player and captain, so the question marks around him are really just background noise."