Oxlade-Chamberlain, 24, joined Liverpool from Arsenal in a reported £35million move on deadline day.
The England midfielder was apparently targeted by numerous clubs, and offered a new deal by Arsenal, but opted to head to Anfield.
Henderson said Klopp could get the best out of Oxlade-Chamberlain, who is into his seventh Premier League season.
“You’d have seen him [Klopp] on the sidelines, he’s very passionate, what you see is a fantastic manager and I think he will help Alex a lot,” Henderson told UK newspapers.
“He will help him develop as a player and hopefully you will see even more good things from him.
“I’m delighted he’s signed for Liverpool, but, at the end of the day, we are with England and our focus has got to be on the game here [against Slovakia] and after Monday then I’m sure we can start focusing on Man City and getting him into Melwood for his first session and stuff like that.”
Henderson talked up Oxlade-Chamberlain’s versatility, saying the 28-time England international could perform out wide or centrally.
“I think he can do both very well, he’s a fantastic player, he can adapt to each position, gives you something different on the wing,” he said.
“He’s very direct and powerful and in the midfield he’s clever enough to get on the ball and get on the half turn so, for me, he can play in either position.”
Liverpool’s first outing after the international break is a trip to Manchester City on Saturday.
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