Gatland coached the last two Lions tours to Australia in 2013 and his native New Zealand last year but says Australian Jones is the best man to handle the next one.
"I'm learning from him. He's doing a great job so I'm watching him pretty closely," Gatland added.
"I'm just intrigued by watching him, the way he coaches his team. You learn as much as you possibly can from everyone. That's part of the game. The game changes and you try to learn as much as you can."
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The pair will meet having overseen a winning start to their respective campaigns with injury-hit Wales doing better than expected in brushing aside Scotland 34-7 in Cardiff, while England finished strongly to beat Italy 46-15 in Rome.
Gatland said the key to winning at Twickenham, where Wales last had success in the 2015 Rugby World Cup, is "confidence and self belief".
"It's about being prepared to play at a high intensity. Play with composure and patience and that's the key. Not being intimidated by the Twickenham factor at all. There are a lot of guys in this squad who will go there with a lot of confidence," he said.
"Everyone talks about how much they dislike the English but I think the relationship between England and Wales has always been close. It's the rugby that brings the two nations together. I think that's what makes the relationship special. I think there's been a lot of respect between the two nations over the years."
Wales named an unchanged starting 15 for Saturday's game. Jones will announce his England team on Thursday but will be without Ben Youngs after the scrum half damaged his knee ligaments in the win over Italy.
(Reporting by Mark Gleeson; Editing by Christian Radnedge)
