Henderson was on the bench for the first two games of the tournament, but came into the team and did well as England beat Wales 3-0 on Tuesday.
He was brought in to provide experience and extra legs in midfield, and Southgate must now decide whether to keep faith with him against Senegal.
The introduction of Henderson gave Jude Bellingham a licence to roam further forward, and the make-up of the England midfield is one of the key selection decisions facing Southgate.
Mason Mount started the first two games of the World Cup alongside Declan Rice and Bellingham, while Kalvin Phillips returned off the bench against Wales.
Henderson was a key player for Southgate at the 2018 World Cup, and his Liverpool team-mate Trent Alexander-Arnold believes the 32-year-old is a man for the big occasion.
“I think he is criminally underrated as a footballer,” said Alexander-Arnold. “He is someone who can influence games. When people think of him, they think about shouting, running and the dirty side of the game, but on the ball, he is technically an outstanding footballer.
“He is a natural-born leader and you can tell it is not forced, it’s completely natural.
“He brings that intensity to the team, he demands it from people with his aura and shouting. The way he plays the game is very intense, and you need players like that.
“He is an all-round outstanding footballer and he deserves a lot more credit than he is given.”
Southgate is also facing a huge selection decision over whether to recall Raheem Sterling or stick with Marcus Rashford and Phil Foden in attack alongside Harry Kane.
Rashford scored twice in the win over Wales, while Foden also impressed with a goal.
Sterling started the first two group matches but was left on the bench for the Wales game, and Southgate has a tough call over a player he has always trusted in big games.
Bukayo Saka also has a case to start, after scoring twice and being arguably England’s best player in the 6-2 win over Iran.
Jack Grealish is another option, although he is likely to start on the bench.
Grealish admits he has sympathy with Southgate, who he believes will be criticised whoever he selects on Sunday.
“It is a difficult one for the manager, because no matter what he does, he is never going to win,” said Grealish.
“Because if Phil does not start, it is, ‘Phil has got to start’; if Rashy does not start, it is, ‘Rashy is on fire, he has got start’. I think it would be nice for people [to cut him some slack], in my opinion anyway.
“He has proved himself as a brilliant manager over the past few years since he has been England manager. He has done well in the tournaments, he has led us again as group winners going into the last 16.”
With the prospect of extra-time in the knockout stage, Southgate has emphasised that more than 11 players will be needed if England are to go deep into the tournament.
Since meeting England rugby head coach Eddie Jones before Euro 2020, Southgate has adopted his use of “finishers” instead of substitutes.
Alexander-Arnold is set to start on the bench against Senegal, but says substitutes in the squad want to make a positive impact.
“One hundred per cent,” he said. “Especially with five substitutions, you can change nearly half the team.
“We need to be ready, especially in the knockout games. The games are going to get tighter and tighter. They are going to be close, close games.
“A lot of the time, games are won in the last 20 or 30 minutes, so everyone needs to be ready to come on and perform.”