That is the view of Gunners expert Charles Watts, who responded to claims that the 27-year-old - who is currently sidelined after surgery - could end his self-imposed exile under the German's regime.
White has not been called up for England since the 2022 World Cup, where he left the camp for personal reasons and was later reported to have had a falling-out with assistant coach Steve Holland, which were denied by Gareth Southgate.
"It's a tough one," Watts told Sports Mole. "It's been quite nice not to have to worry about Ben White getting injured when he goes away with England. But from an England perspective, there's few better defenders in England, certainly right-sided defenders, than Ben White over the last couple of years. He's been so incredibly consistent.
"He's so versatile. He offers an awful lot. He's got brilliant character and personality. He's a winner. He should be playing for England. He should definitely be in the mix for England.
'Ben White will think hard about returning to England'
"Of course, what happened happened, and he's taken himself out of the mix for that. I would expect there's certainly going to be conversations had because a large part of the reason he wasn't playing for England was the previous coaching setup. That's clear. They are no longer in place now. If Thomas Tuchel is open to Ben White coming back, then I would imagine Ben White will think hard about it."
White's apparent quarrel with Holland was allegedly triggered by a barbed comment that the latter made about the Arsenal defender's interest in football, as White has openly admitted that he does not watch the sport at home.
Southgate initially said that there were a few defenders ahead of White in the pecking order, before changing his tune in March and confirming that the versatile defender did not want to be considered for international selection.
White missed Euro 2024 as a result and did not have a change of heart during Lee Carsley's six-match reign, although the 50-year-old left the door open for the Arsenal man to come back into the national team setup.
Watts does not expect White to just flip a switch and decide to reignite his international career when Tuchel takes over in January, but if the former Chelsea boss can charm him, there is every chance that he will pull on the England jersey again.
'There will be conversations between White and Tuchel'
"I don't think it's necessarily an absolute given just because there's been a change in the coaching setup that he will go back," Watts added. "He'll think about it a lot. Ben's a very different type of character.
"I don't think he will look at England and think it's the be-all and end-all like some other clubs do. He loves his downtime. When you go away with England, you don't really get that downtime during the international break.
"He'll have a lot to weigh up, but I do think that the most likely scenario is there'll be conversations had now once Tuchel is in place. If Ben White likes what he hears from Tuchel, which I expect he probably will, he will make himself available."
White has only won four senior caps for England, all of which came in friendly matches, and his last appearance for his country came in a 3-0 win over Ivory Coast in March 2022.
Arsenal had no players involved in England's last two matches against Greece and the Republic of Ireland, as Bukayo Saka and Declan Rice were among eight players to withdraw from the squad with injuries.
Both will be assessed ahead of Saturday's Premier League clash with Nottingham Forest, as will Leandro Trossard, who was substituted early in Belgium's UEFA Nations League loss to Israel over the weekend.