Burke, 24, told The Rugby Paper, "I am my own player but I have the ultimate respect for what Owen has done at Sarries and also with England. He'll probably go down as the greatest ever."
Burke, a former New Zealand Under-20s representative, was in England as part of the Barbarians team that beat Fiji 45-32 at Twickenham in former Crusaders' teammate Sam Whitelock's last game.
"I have not yet spoken to Owen, but I'd love to. It would have been pretty cool if he'd been playing for the Barbarians, but it wasn't to be. I'm sure I will link up at some point.
Burke said he was looking forward to joining the club. He has had Zoom meetings with coach Mark McCall.
"He mentioned things he likes in my game, such as passing, kicking, and attacking, and they fit into the way he wants Sarries to play.
"They are a very strong club, very similar to what the Crusaders are in New Zealand. They have had quite a lot of success having built an awesome culture in order to have that success."
That success was a big part of his decision to transfer to England.
"I didn't intend to leave New Zealand at 24, but the opportunity to make this kind of move might not be there in a few years.
"I spoke with lots of people to get advice on it. It was a big decision but all the advice was positive."
Burke didn't play as much for the Crusaders this year because he was recovering from a torn Achilles tendon suffered at the end of 2023 and underwent a six-month stint of rehabilitation.
"It was my first serious injury and gave me the perspective of not taking the game for granted. You realise how tough it is to have it taken away. But my body is feeling good now and you appreciate your body more."
Burke said he still had ambitions to play international rugby and said playing well for Saracens would help him achieve that.
His mother is English, and her father is Scottish, which opens up two possible avenues for Test play.