With the likes of France and Portugal already out of the competition, Southgate will be looking to write his name in the history books.
The last meeting between these two teams in a major competition was at the 2010 World Cup, in which Germany defeated England 4-1.
Iceland pulled off the greatest result in their history, coming from behind to stun England and reach the Euro 2016 quarter-finals.
On the back of finishing top of their group, England will next face Germany in a mouth-watering round-of-16 clash in Euro 2020.
The English captain, who has struggled to reach his usual heights in Euro 2020, has been linked with a move away from Tottenham Hotspur in the coming window.
England beat Czech Republic 1-0 at Wembley on Tuesday to go through to the last 16 of Euro 2020 as Group D winners courtesy of Raheem Sterling's 12th minute goal.
Tottenham Hotspur forward Kane has been substituted in all two of England's Euro 2020 group stage matches due to disappointing performances.
In-form striker Patrik Schick, is a surprise contender for the Golden Boot with three goals to his name already.
England manager Gareth Southgate made it clear that Harry Kane will start the Euro 2020 game against Czech Republic.
Southgate has a lot to think about, with the Three Lions struggling to score goals while their captain is having a miserable Euro 2020 campaign.