The striker injured his ankle early in the second half of Monday's opening 6-2 victory over Iran in Group B and was later substituted.
"Harry is fine. He has worked slightly separately from the group but all good for Friday night," said Southgate.
"He had a scan [on Wednesday] to make sure everything is fine."
Tottenham’s Kane has scored 51 goals in 76 appearances for the Three Lions, two behind Wayne Rooney's record of 53.
Meanwhile, Manchester United defender Harry Maguire is feeling "much better" after also being substituted on Monday.
"He was feeling ill and that was affecting his vision," Southgate told BBC Sport. "You worry about concussion in that instant, but we were going back through all the footage and there is nothing, so he is in a good area."
Defender Kyle Walker has stepped up his training and is available to play on Friday for what would be his first match since groin surgery in October.
Forward Callum Wilson did not train in a light session with the rest of the substitutes at England's Al Wakrah training base on Wednesday, but is not considered a fitness doubt.
Midfielder James Maddison, who missed the Iran match because of a knee issue, also did not train.
England will qualify for the last 16 if they beat the United States and Southgate added: "We would like to get qualification done as soon as possible.
"The first objective is to get out of the group.
"We would love to do that on Friday, but the game won't be anything like Monday.
"We have to make sure we are back to the psychological place we were at the start because the States will be an athletic team, press really well, be organised, well coached.
"They have quite a few players we know from the Premier League and they showed in the first half against Wales the best side of themselves.
"Monday was a great start and it is that reset to be ready for Friday."
Gareth Southgate’s worriedness
England coach Gareth Southgate’s is "worried" that England appearing as an example at a pre-World Cup referee briefing will have ramifications for his side.
Against Iran, England were penalised for a shirt pull from a corner, whereas Harry Maguire's appeals for a foul at the other end had been ignored.
On day three of the World Cup, a similar incident resulted in Argentina getting a penalty against Saudi Arabia.
"We've got to have clarity or we don't know where we stand," Southgate said.
VAR the only cause for concern
My only slight concern after watching England had nothing to do with their display - it was the part the video assistant referee played in their game.
An Iran defender bear hugged Maguire to bring him down at a corner but nothing was given, which was just pathetic when you consider that Stones conceded a stoppage-time penalty for doing far less.
It didn't matter because we were so far ahead at the time, but imagine if we were 2-1 up and on the wrong end of a decision like that?
We've seen goals ruled out in other games for extremely tight offsides too - someone's toe or shoulder being the wrong side of the line - which I never like to see, and I just hope VAR does not get too involved in this World Cup because we will enjoy the football more without it interfering.
