England captain Kane hit a hat-trick in the 4-0 rout of Bulgaria on Saturday as Southgate’s men made it three successive Group A victories.
The Tottenham striker looks back to his best after recovering from the ankle injuries which plagued him last season.
It was suggested Southgate might want to rest Kane to avoid over-working him ahead of a busy period for club and country.
But while Southgate said he would freshen his side up at St Mary’s, Kane is untouchable after his strong start to the campaign.
“I don’t think you can have a player that is undroppable, because that is a dangerous route for any team and it is not a healthy position for a player,” Southgate told reporters on Monday.
“It is safe to say we won’t be dropping him for tomorrow. His level of performance is so high that dropping him would be a rare occurrence.
“We might freshen the team a bit, that will be important. We don’t need to, everyone is fit and available. We need to make sure we get the balance right.
“We need to get the right attacking and defending profiles to make sure we win the game.”
England were largely in control against Bulgaria after an indifferent first half.
But Southgate is expecting a tougher game against a Kosovo side who are unbeaten in 15 games and still just behind the group leaders.
“We are expecting a different sort of challenge to Saturday but one we are looking forward to,” Southgate said.
“It will be a very different style of game. Kosovo will be very high pressing, hard working, a more attacking threat than we faced on Saturday.
“Maybe there will be more space to play up front. Whatever we learned from Saturday’s game, this is a completely different challenge.”
England’s form under Southgate and their impressive start to qualifying suggests the 2018 World Cup semi-finalists will be among the favourites to win Euro 2020.
England midfielder Jordan Henderson is keen to add a winners’ medal with England to the Champions League crown he earned with Liverpool last season.
“It would mean a lot, any trophy that I win, I will be over the moon,” he said.
“That is all I ever want is to win, whether that’s at Liverpool or England.
“It means so much to me to win trophies or win as a team.
“To win a trophy in the summer was massive and huge for me and my team, for England that is what we want to achieve.
“We want to win trophies and be as successful as we can be. Hopefully one day we can do that.”
