Borussia Dortmund midfielder Jobe was called up to the England squad for the first time for the Nations League matches against Croatia on Thursday and Spain on Sunday.
If the 21-year-old features in either game, the Bellinghams will become the 22nd set of brothers to represent England.
It has been 19 years since Gary and Phil Neville, who both starred for Manchester United, were the last brothers to play together for England.
Real Madrid midfielder Jude, 23, has said it would be the highlight of his career to wear an England shirt alongside his younger brother.
And England Under-21 captain Jobe, who has emerged as a key figure for Dortmund this season, echoed Jude's take on their incredible story.
"I can't ignore it, but obviously with Jude being here too, it's a great, great feeling for the family," Jobe said on Tuesday.
"It's quite special, to be honest. It's such a huge bonus on top of something that's already so special and so great.
"To be called up for England is a dream itself. To have that chance of an opportunity to represent England with my brother, it's really hard to put into words.
"I think it's only emotion that could describe it, and, hopefully, if that time does come, you'll see a lot of emotion from people, and definitely from my family."
Jobe learnt of his selection by England boss Thomas Tuchel last week, with the German revealing that Jude had recommended he take a look at his sibling.
Tuchel said being able to select both brothers was a "beautiful story".
"Yeah, I'd been obviously hoping for it, as you would as a player," Jobe said.
"It was last Thursday when I was driving back from training, and I saw a message pop up in my car and it said, 'Hi, Jobe, it's Thomas Tuchel'.
"I was, as you can imagine, ecstatic and so excited and then when I took the call later on, it was just quite surreal.
"You don't really know what to do with yourself in that moment, but you're just so pleased and I couldn't stop smiling."
Jobe and Jude have followed similar career paths en route to their forever moment with England.
They both came through the Birmingham youth academy, with Jude joining Dortmund as a teenager and Jobe moving to Sunderland.
Jude went on to global stardom in Madrid, while Jobe helped Sunderland win promotion to the Premier League before following in his brother's footsteps at Dortmund.
"I feel really, really proud," Jobe said. "It was something that I'd hoped for and I felt like I was making it a little bit more possible each week."
