"The instructor has also been giving lessons to Harry. It's a great stress-buster."
The workout sessions are said to be helping Meghan cope with the stress of her court case against the Mail on Sunday, as she's suing them for printing parts of a letter she sent her father.
The Mirror reported in May that Adele had befriended the royal couple and was giving them advice on how to get by in Hollywood and avoid prying eyes.
"Adele loves the neighbourhood. She's also recommended her 4-year-old son Angelo's pre-school and discreet places to take Archie where they won't be bombarded by fans," a source said.
Adele recently revealed her incredible weight loss after making changes to her lifestyle.
It's said the transformation had nothing to do with wanting to be "skinny".
UK personal trainer Pete Geracimo said the star's son Angelo was the reason she wanted to lose weight.
He also said the attention her weight loss had drawn was "mind-blowing".
Geracimo recently opened up about his work with Adele on her fitness, holding her to a gruelling workout routine and helping her make better food choices.
"When Adele and I started our journey together, it was never about getting super skinny. It was about getting her healthy. Especially post pregnancy and post surgery," he said.
"When 25 dropped and the tour announced, we had to get ready for a 13-month gruelling schedule. In that time, she warmed to training and made better food choices."