Reports had suggested that Konecki was planning to propose to the 'Someone Like You' singer during her birthday celebrations.
However, Adele took to her Twitter page to deny the claims.
She also took the opportunity to laugh off reports that Rihanna had sent her a birthday cake.
"Had a lovely birthday, thanks for all the messages," she tweeted. "I got a blossom tree! I didn't get a cake from Rih Rih & I'm not engaged, blah blah x"
Adele and Konecki recently bought a £2.5m ($4m) home in Brighton, England, and rumors have also suggested that the singer is planning to invest in a property in London.