The German has signed an 18-month contract with the Football Association which starts on January 1, and Tuchel is well aware that his mission is to add a second World Cup star to the England jersey.
Friday's qualification draw pitted his team against Serbia, Albania, Latvia and Andorra, with the group winners securing an automatic place in the finals in the United States, Canada and Mexico.
Tuchel is a hugely-respected club coach but is new to the international arena and confirmed he planned to set aside time to speak to Southgate, who bowed out in the summer after taking England to a second-successive Euros final.
"He's a gentleman," Tuchel told Sky Sports News.
"We met before when I was at Chelsea and it was a pleasure to talk to him, and why shouldn't I (meet him again)?"
He will also hold talks at St George's Park next month with Carsley, who took interim charge for England's Nations League campaign in the autumn.
"We will work from January at St George's and I hope it will become very regular that we will meet and very normal that we meet," he added.
"Of course we will exchange (ideas) because I'm interested in his point of view about the (squad selection for) the games, about the potential in the group and how he felt about the group and the experiences.
"He is the under-21 coach, so he will be very, very close to me and we have enough time from January."
England are set to start their qualification campaign in March and have won every match they have played to date against their Group K opponents.
However, Tuchel told BBC Radio 5 Live it was not a given his team would top the group, adding they would need to be "serious" and "determined".
The draw pitted Scotland against Greece, who they must also face in a two-leg Nations League promotion-relegation play-off in March, plus the beaten team in the Portugal v Denmark Nations League quarter-final and Belarus.
Asked about the prospect of playing the same opponents four times in one year, head coach Steve Clarke told BBC Radio 5 Live: "We can treat both a little bit differently.
"We'll get to know each other very well I think, so you might find that (by the time of) the World Cup qualifiers, we tend to know each other a little bit better and maybe (they will be) cagey games. But you never know in football, it's very difficult to gauge how it's going to be."
One unknown for Scotland will be the venue for the 'away' match against Belarus. They have been barred from playing at home since Russia's invasion of Ukraine in 2022, which they supported. Northern Ireland played them in Hungary in October.
Clarke wants to go "all guns blazing" into the qualifiers, with all six matches in their four-team group crammed into the September, October and November windows.
Northern Ireland boss Michael O'Neill welcomed the fact his side's campaign would not begin until the autumn, when they take on either Germany or Italy, plus Slovakia and Luxembourg.
"The four-team groups suit us as a smaller nation and it gives us a lot of time to prepare," he told the BBC.
"The June fixtures are difficult for us, because we have so many players who play in the EFL and their season finishes so early, like May 5 or 6, and you're asking lots (of players) to play in internationals sometimes on June 10 or 11. So not having that challenge is a good thing for us.
"We always tend to play our best football in September, October, November, as the Nations League has shown, so we'll be ready for when the games come around in September."
Wales head coach Craig Bellamy was happy to have been placed in a group of five alongside regular recent foes Belgium, plus North Macedonia, Kazakhstan and Liechtenstein.
"It gets the competition going really quick, so that's a real positive," he said.
"It's a good group, but we're going to have to do our homework really well and hopefully try and attack it and finish top of the group."
Wales beat Belgium to reach the semi-finals of Euro 2016, but have not won any of the four subsequent meetings.
The Republic of Ireland have not qualified for a major finals since that same tournament and will be up against the winner of the Portugal v Denmark Nations League quarter-final, plus Hungary and Armenia.
Coach Heimir Hallgrimsson told FAI TV: "I don't think there will be a runaway winner, which makes it more possible to qualify. I think it's an equal group."
Sixteen European teams will qualify for the finals, which will feature 48 countries for the first time.
The 12 group winners qualify automatically, with four other places to be determined in play-offs to be held in March 2026.