The 22-year-old completed his deadline day move from Dundee and is in the squad for today’s lunchtime clash with Kilmarnock at Rugby Park.
Centre-half has been a problem position for Scotland and Rodgers believes Hendry – who did not win any youth level caps – could be the solution.
He said: “In Jack Hendry, I believe we’ve signed someone who is, potentially, a brilliant centre-half not only for Celtic but for Scotland.
“He’s super quick, can defend well and play football. If he can deal with the pressure, scrutiny and expectation of being a Celtic player, he can go a long way.
“There’s no question he could play for Scotland. He just needs experience and he’s going to get that every week he plays here.
“With Celtic, every meeting is a big game. Jack’s done a great job at Dundee and I give credit to Neil McCann for the way he’s got his side playing because it showcases talents like Jack.
“By asking your team to have the courage to play football, players like Jack can exhibit their qualities. The ideal characteristics for international football are physicality, speed, power, technique, the ability to read a game tactically and the right mentality.
“Jack has all of those attributes and we intend to allow them to grow naturally.”
Rodgers insists Hendry is not a long-term project as he can challenge for a top-team place immediately.
He said: “I’d have no hesitation in playing Jack.” Rodgers is pleased with securing Hendry, Charly Musonda, Marvin Compper and keeper Scott Bain in the transfer window, with Lewis Morgan being loaned back to St Mirren.
He said: “We’ve had a great window.”