The One Direction singer, then 17, is said to have been with Lucy Horobin, 32, after meeting at her Key 103 show in Manchester last August, reports The Mirror.
The relationship allegedly took place before he began dating Xtra Factor presenter Caroline Flack.
Horobin had been married for a year at the time of the affair, although she had reportedly been "living separate lives" from her husband.
A source close to Styles said: "Lucy was right up his street, exactly the type of girl, or woman, should I say, he is attracted to.
"She's sexy, confident and is doing well in her career. But he never wanted anything serious."
A friend of Horobin's stated that she later realised she had made a mistake with the affair, but that they had a great time during their three months together.
"She knows she shouldn't admit it but said the sex was amazing. He knew exactly what he was doing despite the fact he was only 17," they said.
"He's adorable and Lucy had a lot of fun. But it was never anything serious. It was a mistake."
The source added: "She wanted to make a real go of her marriage and decided the only way to do that was to confess about Harry. She was terrified of admitting what she had done.
"Although she believes she was separated from her husband at the time, she knew he would hate it. But she knew it was the only way of moving forward."
Horobin has yet to respond the newspaper claims, but has since tweeted a sad smiley face earlier today (June 24).
A friend of Harry Styles recently said that his relationship with Caroline Flack was "just physical".