Southgate has named a 25-man squad which included a first call-up for Leeds striker Patrick Bamford along with recalls for Burnley goalkeeper Nick Pope, Liverpool defender Trent Alexander-Arnold and Manchester United's Jesse Lingard -- who missed the cut from the group which reached the Euro 2020 final earlier this year.
Kane made his first appearance of the season in Tottenham's 1-0 win at Wolves on Sunday and could be involved on Thursday as Spurs host Pacos de Ferreira in their Europa Conference League play-off second leg.
Speaking at England's squad announcement, Southgate told a news conference: "Harry got into the game at the weekend. I'm expecting that he'll play a fair part tonight.
"The good thing from our point of view is it looks as though everything is resolved and settled club-wise now. So he's got a clear focus now and I'm sure he is looking forward to getting out on the pitch with Tottenham and then with us next week.
"I don't know if there might be other players who might possibly be on the move before we meet. That often is the case in September as well. But in terms of Harry's situation, it is settled, it looks like he is going to be a Tottenham and that is obviously fantastic for Tottenham especially."
Rashford is unavailable as he recovers from shoulder surgery but Southgate said he stayed in close contact with the trio throughout the summer.
"I was in touch with all three of them in the days after the final and we've then been in touch with their clubs as well," he added. "Other people at the FA have also been involved in that. They know there's support if they need but also they are very keen to move on. They've got a fresh season, they've got fresh challenges.
"They are all very exciting young players with a lot of exciting times ahead of them and they were all part of an amazing experience across the summer. I understand the question but for them they are very much looking forward."
Southgate's contract expires in December after next year's World Cup with Football Association chief executive Mark Bullingham confirming in June that there were plans to offer the 50-year-old an extension.
However, Southgate said nothing has yet been discussed and he remains relaxed about the situation.
"We haven't had any time for anything of that nature," he added. "I had a week or 10 days here after the tournament, then I was away for a couple of weeks and Mark was away for a couple of weeks so we've really just been focusing on debriefing the tournament and getting on with the preparation for the games this week.
"In my head, I've got to focus on 'what's the priority at the moment?' That's getting the team qualified for Qatar. So, I'm sure at some point over the next few weeks -- I'm due meetings with Mark anyway -- and I'm sure we'll have discussions.
"But in my head, the Autumn for me is about getting the team to Qatar. Everything else can wait really. It is not important. I'm contracted through to Qatar anyway so anything we're discussing is about time beyond that. It is not relevant for this period."
Defenders: Trent Alexander-Arnold (Liverpool), Conor Coady (Wolves), Reece James (Chelsea), Harry Maguire (Manchester United), Tyrone Mings (Aston Villa), Luke Shaw (Manchester United), John Stones (Manchester City), Kieran Tripper (Atletico Madrid), Kyle Walker (Manchester City).
Forwards: Patrick Bamford (Leeds), Dominic Calvert-Lewin (Everton), Jack Grealish (Manchester City), Harry Kane (Tottenham), Bukayo Saka (Arsenal), Jadon Sancho (Manchester United), Raheem Sterling (Manchester City).