Konecki reportedly reached out to his ex at Christmas when he and Adele began leading separate lives.
The superstar, 30, shocked fans when her reps announced on Friday, April 19, 2019, that her marriage was over.
Adele and Konecki, a charity entrepreneur, raise a son, Angelo, together.
But a source said Konecki has been moving on: "Clary was shocked to get a message from Simon wishing her happy Christmas, especially because the news he had split from Adele wasn't out there, but now it all makes sense.
"He messaged again on her birthday in February and wanted to meet for coffee in Hove but she hasn't told anyone if she has met him yet. They have a long history. They were neighbors, then a couple for more than four years before he met Adele. They had the same friends and seemed to have a solid relationship. Clary adored him and it was a shock to everyone when they broke up."
The Sun insider continued, "After the split, Simon moved to LA with Adele and Clary remarried and set up a successful business as a personal stylist. She focuses on practicing yoga and environmental sustainability close to her family in the town she grew up in.
"She has a totally different life to the one Simon had in LA, which he is finding refreshing."
Also, the singer has already moved on with a mystery man, the Sun on Sunday has reported.
A source told the publication, "Behind closed doors, Adele has revealed, 'I'm divorced now, so I'm trying to find my new normal.' "
"Publicly, Adele is saying as little as possible about the split. But, privately, she's been very open about the fact that her and Simon have already divorced. She's been telling friends the marriage is done and dusted."
The Sun on Sunday has reported that the star has been seen kissing a bearded mystery guy in New York.
He's reportedly American and is a dead ringer for her ex-husband.
Konecki could get half of Adele's fortune as sources say she didn't have a prenup.