Evans is desperate to make peace with his 24-year-old daughter, who is expecting her first child with boyfriend Simon Konecki.
Adele was raised by her mother after Evans left the singer and her mother Penny when she was just three years old, Femalefirst reported.
"Mum rang and said, 'Mark, I've got some important news for you. Adele is expecting a child'. My first reaction was a surge of happiness for her. But as we chatted about how Adele had told her in person, it dawned on me that my daughter hadn't wanted to tell me herself.
"My happiness for her turned to gloom because I realised I really was out of the picture as far as she is concerned. I would have loved so much to have been able to hold her in my arms and tell her how happy I was for her... I am begging her to give me another chance," he said.