The Arsenal defender had made himself unavailable for the Three Lions since a high-profile fallout with England assistant coach Steve Holland at the 2022 World Cup in Qatar.
Speaking ahead of Euro 2024, previous manager Gareth Southgate confirmed White did not want to be selected under his regime.
But after starting his new role as England coach in January, Tuchel held talks with White to see if he would be interested in changing his mind.
White was not named in Tuchel's first squad despite recently returning from a lengthy injury lay-off, but the new England boss has now confirmed the defender is making himself available for him.
Speaking to the press about White, Tuchel said: "He'd love to be back in the squad.
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"I just think it's a bit too early now given the seriousness of the injury that he had.
"I'm delighted he's back in back-to-back trainings. Huge compliments to the medical and performance staff of the FA.
"We are honoured speaking to him, speaking to Ben, delighted that he's back on the bench.
"Now it's just a question of getting more minutes, more rhythm. He wants to be back."
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White underwent surgery on a knee injury back in November and is still on his way back to full fitness.
With White set to come back into contention for his country, England legend Stuart Pearce says that time will tell whether White is truly welcomed back into the fold.
Speaking to talkSPORT, Pearce said: "In all honesty, you know the passion I have for my country.
"You have to put your country before yourself. I struggle to see how individuals fall out with the likes of Steve Holland and Southgate."
Pearce then added: "If they let you down once, they always let you down."
The Nottingham Forest hero added: "Tuchel will wipe the slate clean with Ben White and sometimes you have to do that with players.
"Time will tell whether Ben gets back in the squad. I'm always disappointed when someone decides they don't want to represent their country."
White has been limited to just 16 appearances this term as a result of the knee injury suffered in November.
Since returning the defender played 13 minutes in the 7-1 win over PSV Eindhoven in the Champions League, before playing 79 minutes in the second leg at the Emirates Stadium this week.
White will now be hoping to play a key role for the Gunners in the rest of their campaign as they target European glory and a spot in next year's Champions League.